No BC membership, as I do not know what that is?
So a closed circuit is the same race ad a road cicuit, its just closed off to traffic, got ya!
So what memberships or license did you have to get for that? how fast of a rider are you? Did you find it easy to stay with a group?
BC is British Cycling. I would take a look at their website as there's a lot of useful information and everything you could possibly need to know abut the rules and licensing aspect. Results and a calendar of future races are other obvious benefits of a visit to the site.
I can't really comment too much on circuits but the two open road races I did were technically on cicuits but it's not the same as on a purpose built track, which is like a Grand Prix, for bikes. From what I have seen and read, the circuit races or Crits are at a v fast pace and just a series of corners & sprints, corners & sprints... and repeat... Likely a bunch sprint at the end. The ones I did were more strung out but this was in part due to the way the races were organised (split into groups, based upon ability).
I have BC Silver membership but I upgraded my Provisional license to a full racing license for an additional cost of (I think) about £32. This would have meant I kept any BC points, if I had been lucky enough to finish high up enough to have been awarded any.
I am not the world's greatest rider, by any stretch of the imagination and certanly would be out-sprinted by Miss Marple. I am and ok all-rounder and fairly strong at the front, e.g. happy to do a big pull or indeed follow breaks. Stayed with my groups, both times and was involved in a 3 man break in the second race, which was really good fun as we were off the front of the race and being chased down by a field of 57 other riders, including some very good 2nd and 3rd category riders. Foolish but good fun nonetheless
Race one was about 24mph avg and race two was close to 25, if I recall. So it's quite fast but if you are drafting a lot and doing proper through & off chaingangs then it's not as bad as it sounds. Hardest part is making it look like you are doing loads of work while doing as little as possible, which is an art of deception that I am sadly lacking in...