Small.
Buy a scoped .22 and go for squirrels & bunnies.

They're cheap and so is the ammo.

If you find you like it, get a 12ga pump (Like a Remington 870) and go for quail, dove, pheasant, partridge (grouse if you have them) and maybe afterwards, ducks & geese. You can also go after turkey in the fall AND spring.

If you become good at squirrel hunting and have come to love hunting, get a rifled slug barrel for that 870, put a scope on it and get your deer tags... if you can successfully hunt squirrels, you can successfully hunt deer.
To understand why, read a lot of posts here on these pages. Basically, it 'ain't easy sneaking up on a squirrel'.

Welcome to hunting! I wish you the best of luck & God Bless You!