How to get the right tires?

I inherited an old Schwinn road bike, its in relatively decent shape, except for a bit of rust and the tires need to be replaced.
without going to a bike shop, do you have any advice on how to pick out new tires, what to look for, what sizes, material? remember, I am a broke college kid, I just need the bike to get around town and to make it to class on time.

Also any advice on how to remove the rust would be useful.