I really dig scrolling through Palmeto State Armory for ideas on firearm purchases over gun broker. They won’t ship everywhere heads up, but they have a pretty good selection of firearms.

Under 800 can get you a lot of firearms. Not sure why people would recommend a handgun for self defense for someone who can’t carry it as why limit yourself to a handgun in the home. Since you’re new gonna recommend a few that are enjoyable to shoot so you can enjoy shooting to get good reps in:

Any of the Ruger PCCs. Ruger PC or LC carbines would be fun range guns as well as a decent way to defend yourself. Pistol caliber so light recoil but still enough “power” to defend yourself.

With this same idea in mind the Henry Homesteader is a great little gun. Still pistol caliber but more traditional if you enjoy that look.

Beretta A300 may be the best long gun you can find under 800 bucks. It’s a shotgun, so lower capacity and will take more training but no one will argue the usefulness of a 12 gauge. May need to wait for a sale, but definitely worth a pick up.

If you get lucky with a well priced Ruger mini 14 or a used one, I’d snatch it up. Semi auto 556 that is a proven platform. More traditional than an AR but a great gun. You may see some people complain about accuracy due to the thinner barrels especially on older ones, but for home defense distances perfectly fine.