factory should have been 2 1/4 but personally i'd go 2 1/2 or maybe even 3" for the look and sound, and a little extra performance and fuel economy.
what is this cat you speak of? it legally has to be there?
you can put it on, and a high flow cat flows pretty decently so its not going to hurt you much. if your required to do an emissions or a visual inspection then get a cat, if not don't.
fyi if you take it to an exhaust shop they will require you to have a cat, they could get in big trouble for letting a car leave without a cat. a local shop was doing an all out circle track car and the guy was making a big deal about it not needing a cat, it was far from street legal but they still had to put a cat on it, they left it loose and gave the guy a pipe to put in its place, but it was still there.