Don't join the Labour Club - I've heard that the enthusiasm among St. Andrews students for it gets so much that they tend to fold, especially at General Election time! I went to a meeting of theirs a couple of years back and only one person turned up i.e. me!
If politics is your thing, look into the Tories - they have a reasonably active campaign programme and some members of the comittee are seemingly enthusiastic about the task ahead - email them on
stauca@st-and.ac.uk.
The best thing would be to check out when the societies have their pub nights - the Sports ones all have details of when and where they meet.
There are some Academic societies like Astrosoc which are extremely popular, because of a universal appeal (no pun intended!) and they meet every Wednesday for a talk and then do observing in the evening, all of which is free.
www.astrosoc.com.
Go to the Union General Office and get the Societies Directory; it has descriptions of each society and what they do in it.
Good luck.