Frankly speaking "self defense" is kind of a broad topic of discussion. What are the threat vectors you're trying to prepare for? What risk are you trying to mitigate by owning a firearm?
If you're looking to defend against organized armed groups (be it the feds or some post apocalyptic raider group) you would want something in a 7.62/.300 or bigger when it comes to bang for your buck on penetration. Something simple like a CETME .308 (
Century C308) comes to mind, and I believe crazy 3d gun people have some stuff revolving around that platform.
If you're looking to defend yourself in public with some type of concealed carry you're best bet is gonna be a double stack 9mm. I personally like the
Sig P320c but that's roughly 500-700 dollars depending on store and configuration so it's not really in the bang for your buck range.
KelTech and
Ruger both make respectable and cheap(ish) handguns which are good for CC.
If you're looking at home defense you'd want a shotgun or a PCC/PWD. PCC's while cool tend to be pricey for no real reason, like the
CZ Scorpion Evo3 A1 which runs about $1100. But if you want to take the PCC route the
Hi-Point 995 TS is about $450 and will do the job but I would recommend a cheap optic and some type of light. Frankly speaking though shotguns are your best bet on home defense for the money, a farm shotgun with some 00 buck will turn most home intruders into morgue patrons. I personally like the
CZ 712 Utility G2, 5 total rounds, good length. Just gotta hit the fucker.
Lastly is DEFCAD and additive manufacturing. There's some really cool shit in the 3d printed firearms world now. And it's fairly cheap if you already have access to a printer. That being said I can't really recommend you do this, especially if you're a first time gun owner, so I won't link anything on it.
Best advice I can give though it go to a range and try stuff out. Feel on guns is subjective in a lot of ways, especially with feel. Try stuff out that's in your price range before you buy anything.