Get a Remington 870 12 gauge pump shotgun with synthetic stock. This costs around $300. Pump shotguns are highly reliable; automatic shotguns are not as reliable and cost more. A nice thing about this shot gun is it is cheap and ugly. You won't feel bad about tripping and falling face-first into a duck marsh with this shotgun strapped to your back. You'll drain the water out, shuck the action a few times, and continue on your way.
12 gauge is very versatile. It can be used for turkey hunting, duck hunting, coyote hunting, pheasant hunting, squirrel hunting. You may want a 12 gauge that chambers 3" shells or even 3 1/2" shells (2 3/4" shells are the standard 12 gauge shell size -- longer shells typically carry more powder and/or pellets and hence reach out further).
My advice is really a no-brainer. Probably there are other well known cheap and ugly pump shotguns that would serve just as well.
If you become a passionate hunter and begin to hanker for something prettier or maybe an automatic . . . you can indeed do this later. Few of us remain satisfied with one firearm our whole hunting life. Also, even if you move on to other shotguns, this initial shotgun can remain useful in a backup role or for when you are going into a nasty, dirty, inhospitable hunting situation where you don't want to take your beautiful walnut stocked shotgun.