Calshot should have rental bikes (says so on their site). So by far the cheapest way is to rent for a few sessions.
http://www.hants.gov.uk/calshot/cycle.html
After a few sessions you'll know whether you like it and then you'll be better informed as to what you need. You can also get a sense of where folks scored their bikes from; there may be a club notice board as well as a host of fellow trackies who can help you out.
As Calshot is quite steep, I'd take the advice of riders down there as to what equipment is needed (short cranks, high BB, stiff wheels probably).
There some great shots of Calshot as well as further info here:
http://www.britishcycling.org.uk/fea..._calshot.shtml
BTW I've seen people doing the beginner sessions at Herne Hill in clips, straps and trainers.