Oxford is not a large City, and the Law Faculty is accessible without much hassle from every college. Wadham is my college, so I am naturally very fond of it indeed. I love its buildings, its gardens, its role in scientific breakthroughs in the C17, and its tradition of liberalism, debate, and enquiry. I also, by the by, like the King's Arms pub, which Wadham owns. Wadham has not had a good bar while I've known the college, and the current bar is even worse than the last two bars, neither of which was much good. The KA used to be, and maybe still is, the de facto Wadham bar.
Catz has a lot going for it, I think. I am, as I've mentioned above, a fan. Both colleges are quite large in terms of student numbers,and I am sure that you would find diversity at both, and indeed at any college. I again stress that most people enjoy their colleges. Some people don't, and indeed some people don't enjoy Oxford at all, but it's possible to have a bad time (as well as a good time) at any university.
I shall be frank: I have some reservations about Wadham at present, for reasons to do with contemporary cultural politics and the impact thereof on the Academy. Suffice it to say that I prefer Susan Neiman to Slavoj Zizek.
Oxford chatter (which may not amount to much) suggests that Wadham is seen as having set itself somewhat apart from the rest of the university. I have heard people refer to "the Cult of Wadham". Some of Wadham's students appear to be more than usually oppositional to the institutions (college and university) which they have chosen to join, and there might perhaps be an element of tribalism, conformity and, to be blunt, illiberalism amongst the attitudes of the student body.
I think that an Oxford college should exemplify the values of the Enlightenment, and this Wadham has always done; but I share Susan Neiman's concern about erosion of Enlightenment values at leading universities. My daughter is shortly to start at Oxford, and I am actually rather glad that she isn't going to Wadham, which is a strange thing for a passionate Wadhamite to say. I am not sure that Wadham is currently at its best. I hope that this will change. Other opinions about Wadham are available!
My understanding is that the Wadham SU (Wadham's JCR is called the SU) may provide some funding for student healthcare matters. The college itself is bound by its charitable objects to spend money mainly for educational purposes.
I suggest that you visit perhaps four to six colleges and try to get a feel for each, remembering that you might end up at a college you didn't apply to, or of course at another university altogether. Maybe try a mixture of large and small, old and less old. Location isn't mega important, I suggest, because everywhere in Oxford is fairly close to everywhere else.
The main message is not to get too hung up about college X or college Y, for reasons already mentioned. The main thing is to work hard and get into Oxford if you can. If you don't get in, go and have fun and flourish at one of the many other good universities in the UK. I wish you luck!