You'll probably get more help than you need ! So here goes another ...
I'll echo several of the previous posts. Right now is a great time to catch a "sale" on a new shotgun combo package. My preference would be a Remington 870 that can handle up to 3" shells. You can buy this shot gun with a "slug barrel" and a smooth bore with the option of using "Remchoke" screw in chokes. You'll ahve a one gun arsenal that will take you from deer to turkey to duck to dove to quail hunting. The slug barrels are well made and the better sabot slug ammo can provide you with a deer lethal set up that is good to 150 yards and maybe beyond with some practice.
The smooth bore and "Remchokes" in Improved, Modified and Full will work for about any other hunting. I don;t think that you can stay within your $500 budget if you need a scope. Might be the way to go now is do the slug-scope thing for deer season ... if deer hunting is your thing, then the smooth bore later. Maybe Santa Clause ???
Come spring, you can opt for a "turkey choke" if you want to spend the extra $$ and end up with a turkey killing outfit that can drop Toms at 40-50 yards.