Sometimes it actually is necessary to bath a cat. I've had to do it a number of times. The last time was when Gaga had one of her seizures, and was basically covered in pee afterwards. I don't think it does much for a cat's dignity to smell like pee for a week or two
She screamed bloody murder when I was wiping soap followed by water onto her fur, but 5 minutes later it was like nothing happened. Deep down I think she appreciated it. But other than cases like that... nah, no bathings. I have heard that it is harmful to cats (their skin and their coat). They do make shampoo products meant for pets (cats and dogs), so it doesn't hurt to have a small quantity of that lying around in case you need it.
As far as trimming claws... nah, I don't do that either. I actually used to keep my moggies claws trimmed, and I started doing it with my bengals (like others have said, doing two or three nails at a time when they are snoozing), but I decided not to do that anymore because it was hindering their ability to climb, and I've tailored my home to encourage them to climb, so it no longer made sense.
One thing to consider is that it's one thing to try to clip a kitten's claws, or give her a bath, or brush her teeth. But imagine when she becomes a stubborn, 12lb adult. That is a whole 'nother story!