Both are valid ways in to caving, but club caving would be a cheaper if longer method. You would also get more of the social side of the sport, and a number of people to cave with in the future.
A compromise could be a guided starter package where you will get the intense high quality training and experience you would expect, and advice on which clubs are active in your home area / caving area of choice. You could then join a club to expand you skills and experience. There are many professional people out there, and good clubs as well who will on occasion "buy in" outside trainers at a subsidised rate for their members.
Which area are you based in / want to cave in?