I am planning on buying my first telescope. I am getting an 80mm refractor and a 114mm reflector for the same price range. Which would be a better option? Further, would a Barlow lens solve the chromatic aberration issues with a f/5 refractor?
The refractor will be better for wide-field observing of starfields and big nebula and galaxies. For planets and small to medium (also larger with 2" eyepieces or just 1.25" eyepieces with a low magnification and big apparent field of view) sized DSOs (nebulae, galaxies and star clusters) the reflector will have an advantage due to its aperture. The only downside of the reflector is collimation. The reflector will be equal to a 90-95m refractor.
Fast reflectors (low f number) will suffer from coma (f5 will be ok) and fast refractors suffer from chromatic aberration (at f5 this will be a problem for planets, the moon and brighter stars). Some find the chromatic aberration a problem, and some don't.
If your goal is to observe very large nebulae, open clusters and star fields, then I would advise the refractor.
For planets, deep sky objects including planetary nebulae, globular clusters, all the small-medium sized deep sky objects and larger nebulae and galaxies (if the reflector is f6 or lower).
If the reflector is f8 or more it will be harder to find objects and to observe the bigger deep-sky objects.
Further would a Barlow lens solve the chromatic aberration issues with a f/5 refractor.
I suppose in theory they could, but they would have to be designed to do so. In practice, they vary widely in quality, and either don't have an effect on chromatic aberration, or actually make it worse.
Which would be a better option?
There is no objective way of answering this question. Based simply on price per square unit of aperture, a reflector is more economical, and therefore better. But if you're looking for a telescope that doesn't require collimation, a refractor might be best. You have to consider the portability of the specific models you're considering as well. Finally, what would you like to see with your telescope? A high-end refractor with correcting optics is, in theory, better than a similar reflector for high-quality imaging of planets. Ultimately, the best telescope is the one you're comfortable using regularly without feeling overwhelmed.
The optical scheme doesn't matter for beginner. All you need is design which is well used by community, so you don't run into "blurry image" problem with "noname" scope. I recommend you to use the so-called "white lists" of telescopes. Plenty of those exists, many of those are connected to live communities. I do not advocate for any in particular.
Barlow lens does not solve anything except of elongating focal length of condensing light ray. You loose view angle but gain "dirty magnification" and loose more brightness because of two extra surfaces for light.
Do not fall for price. Fall for proven design with emphasis on "plug-n-view".