I've got 8 cats at my house currently--our two plus a mother and month-old kittens we are fostering. They don't really do anything bad with the tank. I have a very hyperactive cat who loves to jump up at the fish as they swim past; they actually play with her. When the fish see her near the tank, they follow her around like they are teasing her. She has a chair in front of the tank so she can sit and watch. I would just recommend having a canopy of some sorts on top for safety, especially if she gets a kitten, because I wouldn't want to see it fall in when no one is around to rescue it if it can't get out. And make sure it won't be able to rub against your light bulbs and burn itself--I had a friend whose girlfriend's cat would always crawl under the metal halide lights to drink out of his saltwater tank (It had some sort of a thing for saltwater...?) and would burn itself on the bulbs.
Cats can be trained, if not quite the same as dogs. Get a squirt bottle filled with either water or if that loses its effectiveness, put vinegar in it. When the cat does something you don't like (getting on the countertop, scratching the couch, messing with the fish tank...) say no loudly and then squirt the cat. Very quickly they will learn what no means, and learn what their boundaries are. I've got one that pushes me all the time; she will jump on the dining room table where she's not allowed and look at me with that big-eyed innocent face, but when I yell no, she jumps right down! I've had a lot of cats, and she's probably the most trouble I've ever had from one, just because she tests authority all the time.