Umm..... Closets aren't a good space for guinea pigs. They need air circulation, which they won't get there, and you won't be able to see them to interact with them, which is the whole purpose of having a pet.
As far as your cats go, cats and guinea pigs can coexist quite peacefully. Unless your cats have an overactive prey drive, they won't bother adult guinea pigs. Adults are too large to interest cats. Pups, on the hand, dart around like mad and look like mice, so the cats can go after them.
One other thing concerns me. If you're having trouble getting together the money for a cage, what are you going to do about vet bills? Exotic vets are scarce and expensive, and guinea pigs can downhill in a big hurry. Once one is sick, it's too late to worry about where you're going to get the money. Do you have a plan for saving money for medical needs?