TL;DR: get the telescope with the largest aperture than you can afford, can physically move, and have space to store.
This will be a Dobsonian between eight and twelve inches.
When I bought my first telescope my main considerations were budget and the light pollution where I live.
When you live in a light polluted place then you'll need a wide aperture in order to gather as much light as possible.
When you have a tight budget then you'll want most of your money to go towards the optics.
The mount is important, too: there's no point having great optics but then not being able to point the telescope at the things you want to look at.
This basically narrowed my choices to a Newtonian reflector on a Dobsonian mount.
A reflector is the cheapest way of getting a large aperture. A parabolic mirror is a lot cheaper to make than a refracting lens.
Just look at the prices of even the most basic refractors, and see how quickly they increase as the diameter increases.
A Dobsonian mount is the cheapest and most simple way of making a mount.
User123 has already given a good answer to your question, but I'm going to disagree with some of their points:
- An eyepiece is often better than a bigger telescope
It's the telescope which gathers light, and this is fixed. A good eyepiece won't make a bad telescope any better, nor will it make a small aperture able to gather more light.
A telescope and eyepiece combine to create an optical system, and it's this system as a whole which should be considered.
What a good eyepiece will do is to ensure that that part of the optical system will perform at its best.
And what is true is that you'll probably end up spending more on eyepieces than on telescopes, long term! :-)
However, you don't need to worry about eyepieces right now. A mass-produced Dobsonian will come with two eyepieces in the box: usually a 2" low power Erfle eyepiece of around 30mm focal length and 70° apparent FoV, and a 1.25" high power Plössl eyepiece of around 9mm focal length and a narrow apparent FoV.
These are just fine to get you started. The best thing to do is to use these bundled eyepieces for a while, until you gain some experience, and then you'll know what you'll want to improve.
(You might still want to buy an eyepiece along with your telescope, though, and if you do then I would suggest you get the Baader Hyperion Zoom Mark IV, in the bundle with the Barlow lens attachment. This single eyepiece will offer you maximum versatility: it'll let you go for high magnification views when your seeing allows, and allow you to zoom out to be able to easily reacquire your target when it drifts out of view. Its only drawback is a relatively low FoV.)
- Consider what you want to observe
If it's your first telescope then you'll want to observe everything!
To look at everything then a Dobsonian is a good all-rounder: long focal lengths for good high-powered views, and 'fast' focal ratios for wide field views.
I consider Maksutov-Cassegrains, Schmidt-Cassegrains, and long focal length refractors to be specialist telescopes. Great for looking at solar system objects, globular clusters, and planetary nebulae; but the FoV is too narrow to observe extended objects like large nebulae and open clusters, and it can be hard to find targets - especially without a good (expensive) Go-to mount.
Short focal length refractors give great low power wide views, but don't go very high.
One of these will be the second or third telescope that you buy, once you've gained some experience and you know that you specifically want one.
"Second or third telescope"? Yes...if you stick with the hobby then one day you'll buy another telescope. Most amateur astronomers have at least two telescopes, and will probably be planning on buying even more in the future.
(Personally, I spent a few years with a ten inch (250mm) Dobsonian, but it's not easy to travel with, so I bought an 80mm refractor to be able to take on a plane; and I'm considering getting a 130mm Maksutov for those high-power views of planets.)
I agree with pretty much everything else User123 says, though :-)
Get a Dobsonian with a magnifying finder scope, rather than the one with the red dot.
A red dot finder is fairly worthless on a Dobsonian - especially under light polluted skies - it doesn't magnify the view so doesn't show you any more. If you want a non-magnifying finder later then get a Telrad: it has markings which help measure distances and position the telescope to find things.
Also consider the mount. Not all Dobsonian mounts are equal. You're going to be moving it left and right and up and down a lot. Compare reviews and see what they say about the mounts.
Generally, the bigger the trunnions the better - a larger surface area there will give a smoother up-and-down (altitude) movement.
When I bought my GSO 10" Dob, there were two options: the standard and the "deluxe". I went for the deluxe version because the mount was improved: the standard version had a simple Teflon pad in the base for the left-and-right (azimuth) movement and smaller trunnions, whereas the deluxe had a "lazy Susan" plate with bearings and larger trunnions.
Finally, forget about astrophotography for now. Sure, buy a cheap attachment which will let you position your phone above the eyepiece and take some photos of the Moon and Jupiter, but you'll need to buy more equipment to be able to take photos of the fainter objects out there.
This isn't to say that astrophotography with a Dobsonian is impossible - not at all: I've dabbled in it myself - but you'll need a very sensitive camera and use a different technique, and the really faint objects will still be out of reach.
If you want to start doing astrophotography then it requires completely different equipment to visual astronomy: it's all about the mount. Spend a lot of money on a mount, put a small (50-70mm) short (f/5 or less) refractor on it, and use a colour astrocamera with it.
Then get used to spending more time processing the resulting data than you did capturing it.
After that, move up to a monochrome astrocamera, lots of filters, and bigger telescope, and a bigger mount.
It's a rabbit hole and a money sink.
Halfway between visual astronomy and astrophotography is electronically assisted astrophotography (EAA).
This is where you use an astrocamera with a very sensitive sensor with a program which does "live stacking" (on Windows this program is usually SharpCap, and on Linux it's ASTAP).
This gives almost instant results, and under light polluted skies can be the only way to see some objects.
I personally have seen some galaxies using this technique which are otherwise invisible to me.
Buy an eight, ten, or twelve inch Dobsonian. All of these will be about the same length - they're usually: 8" F/6, 10" F/5, 12" F/4.
A final consideration is that the 'faster' (shorter focal ratio) the telescope, the more expensive the well-corrected eyepieces. Reflectors suffer from "coma" - a stretching at the edges of the view which is more pronounced at shorter focal ratios.
You can buy a coma corrector to correct this, but again, that's even more money. (Sometimes it feels like it never ends! The initial $800 budget easily turns into thousands spent over a few years!)
Check the classified adverts in your area if you don't mind buying second-hand. You'll save a lot of money doing this. On the other hand, until you have some experience it'll be hard to know what issues to look out for with second-hand equipment.
If your budget is a hard budget then go for a slightly cheaper telescope so you have some left over for accessories - the book Turn Left at Orion, for instance, is a good companion to a first telescope.
If your budget is a soft budget then blow it all on the telescope and then in a few months you'll get to know what additional bits and pieces you'll want.
Finally: good luck and have fun!