I am very squeamish should I get a cat?

I have OCD(about cleaning only) and my kids are dying for a pet kitty and (even I love cats) but my problem is I'm so scared it's going to poop on the floor or drink from the toilet which would problably make me throw up and clean up the whole entire house. It would also bother me alot if I saw the cat walking on the counter or the table. My neighbor told me her cat always steps on the poop in her litter box and gets it on it's paws and I thought that was really gross. Otherwise I love cats and I don't mind taking care of them, even if it means I have to clean it's litter box. I'ld probably consider investing into an automatic self cleaning one. I think those are the major problems I would be worried about getting a cat and I would prefer to get a cat than a dog or any other pet. Any suggestions please.