A simple rule for the maximum magnification is: 2x the aperture in mm. In your case, that makes it 260x. But that's more like a guideline, since it's affected by so many factors. Speaking in general, trying to exceed it almost never provides any benefits, with some rare exceptions (high quality instrument, perfectly collimated, under a very stable atmosphere, observing close double stars - is one possible exception that comes to mind).
So eyepieces shorter than 2.5 mm (after dividing it by the barlow magnification, if any) would likely not be beneficial for you. Combined with your 2x barlow, that means eyepieces no shorter than 5 mm (+/- 1 mm, depending on some factors). In practice, such short eyepieces are pretty rare anyway.
There is also a longest usable focal length for eyepieces, which is the shortest usable focal length times 12, more or less, or about 30 mm in your case (plus or minus some change). Any longer than that and the exit pupil (the diameter of the ray of light exiting the scope) would be greater than the pupil in your eye, leading to loss of light and diminished performance. That's the theory. In practice, there's just not much benefit going much longer than that, as you will find out if you try.
So stick to the 30 ... 2.5 mm interval, give or take 10 ... 20%. These limits are not set in stone, but you will rediscover them on your own, given enough time.
A minimum of 3 eyepieces, and a maximum of 6 or so, should cover most use cases. But a lot of people just end up accumulating eyepieces over the years, or keep trading them.
Look into eyepieces with a wider apparent field of view. A typical Plossl gives you about 50 degrees AFoV. But the view is more interesting, and the scope is easier to use, in a wider AFoV.
As an example and a place to start, I've used the Explore Scientific 82 degree series, which provide 82 degrees of AFoV. Large objects like the Moon or some nebulae or clusters look spectacular in such a wide eyepiece.
It's not mandatory that you strive for a bigger AFoV, but it can be worth it. Also, lenses such as the ES82 series could be used even with high end telescopes, if you ever decide to upgrade.
130 mm of aperture is definitely enough for a lot of fun.
Jupiter will show off its equatorial belts. On a good night you will begin seeing swirls in between the belts - I did that with 150 mm of aperture when seeing was good, and you're within a rounding error from it. You will also see the 4 big moons of Jupiter, but only as little dots. Use medium-high magnification, don't push it too high, because Jupiter is low contrast and it washes out easily at high mag - just try and see what works best.
Give it time and allow your eye to adapt. I believe your scope can track, so enable tracking, relax, breathe calmly, and just take the image in over time. In a couple minutes, your brain/eye system will begin to adapt, and you'll start to see more details. Allowing some time to pass is especially important with low contrast objects like Jupiter, where details are so close to the eye's performance limits.
Saturn will show you the Cassini division in its rings. You will also begin to see some equatorial belts on the planet, but just barely. High magnification is useful, but not necessarily the highest.
Mercury and Venus will show phases like the Moon, but no details beyond that.
Mars can be observed for a few weeks every 2 years, at oppositions; there's a big opposition this year (2018) in the summer. It requires the best seeing (the most stable atmosphere), excellent collimation, and the shortest eyepiece (highest magnification) your telescope will take. Whichever polar cap is pointing at you should be visible, as a tiny white dot sitting on the edge. I have seen the Hellas Basin as a large, bright, white spot when it was full of frost or fog (not sure which), but it melts away quickly. Syrtis Major is probably easiest to see, as a dark, almost black line.
When seeing (air turbulence) is bad, Mars just doesn't work; it looks like an orange pill with no details. Either take a road trip to whichever part of the country has better seeing at that time, or use lots of patience.
Uranus and Nepture can definitely be seen in 130 mm. At high magnification, you will see them as tiny disks, clearly (but just barely) bigger than any star nearby. Uranus is a pretty blue-green shade, Neptune is a deep blue, almost indigo.
The Moon will provide endless entertainment, because there's so much to see. Zoom into a feature using high magnification, or zoom out and observe the whole thing at low magnification - it's fun either way.
For the planets and the Moon, what's important is the so-called seeing, which is the inverse of turbulence:
When seeing is good (turbulence is low) then you can push the magnification all the way up to the limit. When seeing is bad, you have to reduce magnification, or else the image is soft and foggy. Mars only works well with the best seeing; it is possible that seeing might be consistently bad for the whole duration of an opposition - or it could be consistently good. It's weather basically, so it does whatever it wants to do.
Use the Clear Sky Charts site to get a seeing forecast:
On that site, select a location closest to your home. Use the Seeing line in the chart for an estimate. Keep in mind this is weather forecast, so it's not always 100% accurate, but usually it works well enough.
When seeing is good, observe planets. When seeing is bad, observe DSOs (deep space objects, like galaxies, nebulae, star clusters).
Light pollution does not matter at all for the planets or for the Moon. You could observe these objects from the biggest city and they look about the same.
Another important thing for planets is collimation. Read your scope's manual and practice what they preach. A scope out of collimation may severely underperform. It could mean the difference between seeing and not seeing the Cassini division. See here for some examples:
There's a bewildering variety of tools and techniques for collimation. Start with the simple stuff (the manual) since it's better than nothing. Then keep reading. Here's a good page:
Or see here:
A laser collimator should in theory be one of the easiest and most precise tools, but beware of lasers that are not centered. Plug the laser in the focuser, and turn it (spin it) in place. Watch the laser spot on the primary mirror. If the spot moves in a circle as you keep turning the laser, it's not centered. Some lasers have adjustment screws for centering, some don't. High quality lasers like the Howie Glatter series are very precisely centered from the workshop and don't require adjustments.
I do own more complex collimators like the CATSEYE system, but in 99% of cases I just use a Howie Glatter laser with a 2" TuBlug to do a quick check-up before each session. Any laser is fine as long as it's precision-centered.
Collimation is something you'll keep learning for a long time, so don't worry, do what you can at first, and slowly refine your technique over time. But keep your scope collimated. Once you're comfortable with the technique, it only takes 5 minutes.
Air currents in your instrument can also affect the planets and the Moon. These are due to your scope being at a different temperature from the air (because it was stored indoors). The effect is like observing under bad seeing conditions.
The cure is easy: take the scope outside 1 hour before you begin your session, and let it "breathe". A scope at thermal equilibrium with the air has no internal convection.
Your scope is probably not big enough to require a fan on the primary mirror, for forced convection, but you can definitely experiment with it if you like. At your aperture size this is low priority. Fix everything else first (collimation).
DSOs (deep space objects) should be visible in your aperture, especially given the dark sky you're enjoying. More aperture is better, but the level of light pollution is also important. You are very lucky to have such a great location for DSOs.
Pretty much the whole Messier catalog, over 100 objects, should look great in your scope under a dark sky. Among the easiest objects, my favorites are: M31 (the Andromeda galaxy), M13 (the Hercules Globular Cluster), M27 (the Dumbbell Nebula), M57 (the Ring Nebula), M42 (the Orion Nebula).
But since you live under an ideal dark sky, you could just plug a low magnification eyepiece in it and slowly browse the sky. When you see something interesting, stop and switch to somewhat higher magnification. Chances are you'll stumble upon many DSOs this way. I do this with binoculars (low magnification) when I go to Death Valley, and it's amazing what you can discover randomly this way.
Different DSOs require different magnifications, from low to high. You'll just have to experiment and see what works best in each case.
Seeing, collimation, thermal equilibrium don't mean a whole lot for DSOs, because they are fuzzy and low detail to begin with. But a very dark sky helps a lot.
You could also observe the Sun. Get a white light filter, the kind that fits on the top of your telescope, covering the whole aperture. Filters made from the Baader Solar Film are best, they are very good performers and tend to be cheap. Either buy the Baader foil and make the filter yourself, or purchase a complete filter.
Just make sure the size of the filter fits the diameter of the OTA (the main tube) of your telescope - NOT the aperture size, but the external diameter of the OTA.
This will allow you to see sunspots. You can also observe the transit of Mercury over the solar disk, which happens once every several years. I think the next one is in 2019. You can also observe solar eclipses this way.
If you need to use the finderscope when observing the Sun, then make a small filter for it, too. I made some cute little solar filters for my finderscopes from Baader film and white plastic tubes used for sprinkler systems. Cheap, but effective.
Obviously, never point the scope at the Sun without the full aperture filter. And make sure the filter doesn't fall off. Or else all sorts of mayhem may ensue, up to and including someone losing an eye, or the house burns down, etc. Not kidding. Unfiltered, the solar energy coming out of the scope is like a plasma torch.
Buy a book called Turn Left At Orion. It will get you started with how to find and observe DSOs, complete with instructions on which time of the year is best for each object, how much magnification (this is a bit subjective), etc. It's a very good book, I highly recommend it.
I would go with either a sturdy hardcover edition, or the spiral bound one - something that works well out in the field, not some snowflake paperback.
A planisphere is a good thing to have. You only use it 5 or 10 minutes each night, but it will quickly get you oriented in the sky when you do.
When reading the book or the planisphere, use a red light at the minimum intensity that allows you to read. This will preserve your night vision. There are many red flashlights out there made for astronomers, that allow you to dial down the intensity. This is only needed for DSOs. Night vision does not matter for the planets or the Moon.
It's probably beneficial to get a small sky atlas too. Let's say you read in the news that a supernova has been discovered in a nearby galaxy, and it can be seen by amateurs. You could point the scope in its general direction, but you'll need a detailed local map of the region. The one point of light that is seen in the sky but is not seen on the map is the supernova. It also helps when observing other transients such as comets and asteroids (again, they stand out because they are not on the map). Finally, with some smaller DSOs it makes it easier to identify the object from the stellar background (and they should be marked on the map because they are permanent objects).
You could also use various digital maps on a portable device, but I recommend that you master the paper maps first.
Once you own a handful of eyepieces, a barlow, etc, you should keep them together in a carrying box. Many astronomers use a pluck foam case, and they just shape the foam to hold each and every component. I've never used the dividers that come with the case, since optical components are small, lightweight, rather fragile, and should be surrounded only by foam.
Another item I've found useful is a tiny folding table. It doesn't have to be huge, just big enough to hold a book, the sky atlas, etc. It's better than making a pile of stuff around you on the ground.
A cheap, collapsible barstool or something like it would help with long observing sessions. Definitely beats hunching over the scope for hours. Just make sure it's the right height. Big dobsonian owners tend to make or buy so-called observing chairs, which are adjustable, but those are probably overkill for you since your eyepiece doesn't move around that much. Your scope has a geometry similar to my SCT, which doesn't really require a true observing chair, just anything to sit on that's the correct height. Now if you had a big dob then that would be different.
A pretty common improvisation is an empty box or frame that's 3 different sizes in all directions (length, width, height). That allows some height adjustment, and it's pretty cheap to procure or make. Between sessions you could use it to store the telescope or something.