AR-15 in 5.56/2233 is a narrow spectrum weapon with a SINGLE fucking purpose, the OP (who is a faggot) asked about universality and you recommend a single purpose assault rifle? One track mind with these kids today.
The only real answer is the pump action shotgun, good for hunting at limited ranges, is cheap and reliable, good for self defense, wide range of ammunition, easy to maintain. What the 12 gauge pump lacks here and there it makes up for in universality. Target shooting is clays, not bullseye, but you can get in a lot of useful practice with a shotgun. Ammo is cheap enough and available everywhere. The pump shotgun is also a beautiful thing, rounding out OP's list. $350< can buy something that works great.
In a handgun, a 44 Magnum revolver. It can hunt with full power rounds, you can choose lighter loads for self defense and light 44 Special loads for bullseye target. Broad spectrum weapon, I would not go any lower than an 8 shot 357 Magnum in an N frame, max loads really aren't hunting grade but might sneak under the radar. Either choice gives you great reliability with match grade accuracy. Target auto loaders are too tight for anything but hunting and target stuff, combat auto loaders are usually not that accurate, either auto loader style tends to limit ammunition for reliability purposes. Only thing is quality costs money in revolvers, so budget might be an issue.
If you include hunting in a rifle option, 223/5.56 is out, its not even legal for deer hunting in many places and it really isn't a deer rifle. Look up modern scout rifles, or a standard military surplus bolt action (even if the prices are inflated) because it can hunt, it can still be a fast and capable self defense rifle with training (and a super killer with hunting bullets), ammunition is available and companies like PPU make sure even 8mm Mauser, 7.62x54R et al are affordable and for order, aesthetics are there. Learn to handload and battle rifle cartridges can be used for smaller game with lighter bullets and correct loads, can be used for large game.
If you demand an auto loader, consider the CETME, maybe. I've heard poorer things about accuracy which might make it less of a viable hunting option, but its affordable. In any case, 7.62 NATO is far more universal than 5.56 in usefulness.