Don't know where to go in VA.
Rent a gun, Never heard of such a thing. Buy a used 22 rifle either a long rifle shooter or mag shooter, 20 ga. or possible a 410.
Yes you need a knife, I like to have a box cutter handy. I also like pruning shears to cut the legs off. Do a You Tube search for skinning a squirrel.

You need clothing for the climate, squirrels do move about a lot in the rain so rain gear is handy to have.

Al