I first picked a selection of good Universities based on RAE (Research Assessment Exercise) scores and then chose the one I felt most at home at when visiting. The important thing I think is that you are comfortable, you have to spend 3-4 years of you life there so you should be happy.
Apply to courses that interest you at Good Uni’s, there are many not just Oxbridge, and see how you feel about each.
like Ben says, the best thing to do is visit a few places and see how you feel about them.
One thing that’s important, but might not be obvious, is that there’s a big difference in experience between universities that are organised around colleges and those that aren’t.
The plus side of collegiate universities is that it’s very easy to mix with a lot of people doing different things. For me, that was one of the best things about being at Oxford. (There were only 6 people in my college studying physics, so almost everyone I knew wasn’t a physicist). Also with colleges there’s usually a lot of particiapation in sports etc because you don’t have to be very good to get on the college team!
The flip side is that colleges can be a quite claustrophobic sometimes, as you see all the same people all the time, and you don’t get quite the same experience of living as a student, because things are usually quite well organised for you. I did my PhD in a non-collegiate university, and loved that too.
So, I wouldn’t say one is better than the other, but there are differences, so it’s worth doing a bit of visiting if you can and talking to current students to get a feel for it.