Thanks for the replies! After I posted this thread I looked on Amazon again, and stumbled across some 7'x10' $30 rugs with actually decent reviews, so I just went ahead and purchased them.
I don't have any downstairs neighbors, so the noise isn't an issue for us. I would just leave the place uncarpeted, but the finish on the floor isn't that good (IMO) and my cat's claws have been making light scratches in it just from running around, so I really do have to put something down.