It's really is a difficult one this!
It depends very much on your own technical/practical ability (do you want to build/prepare/develop your own bike as a project or will you be paying someone for tuning work) and what type of bikes you are interested in. The 'classic' period still only runs up to 1972 (1967 for 2 strokes), but a large part of CRMC meetings are now made up of 'Post Classic' races for 1973-81 and 1982-86 bikes. 2 or 4 stroke, four strokes cannot be liquid cooled (GSXR750s will be ineligible from the middle of the year after a rule clarification on oil cooling at the AGM).
The cheapest way to start is probably the new post classic production class (as advertised in Practical Classic magazine, they are sponsoring the races) but as I said, they may not float your boat if you want something older and a project to develop as it is a true standard production class.
Classic classes, the up to 200cc class is well supported and seen as a good way to get into it, but not much good if you are a big lad (or lass)!
Any of the group 2 classes can be reasonable if you do your own preparation (road bike based, but period mods allowed, so pretty much anything goes within reason) but paying someone's wages to prepare your race bike is never going to be cheap!
Have a look on
http://www.k21.co.uk/smf/index.php which is the forum which used to be afiliated to the CRMC but is now a seperate entity. Lots of helpful advice (and banter - don't take any of it too seriously!) and contacts as there are class representatives for all the different classes, so these are good people to speak to before taking the plunge.
If you can make it, come to Pembrey over Easter. Everyone (well almost) in the paddock are approachable (unless they are in the middle of an engine rebuild or about to go out to race!) and happy to chat about their bikes, etc, it's a good way to make contacts and get a feel for it and get to see what the different classes are like and which bikes do well.
And there's always lots of stuff coming up on flea bay, depends what you call cheap! I alsways felt that the advantage of racing classic bikes is whatever you spend (unless you go really silly) you will probably get back, because the bikes/parts on them are still competitve years down the line (unlike modern stuff which changes each couple of years).
Best of luck!