Club Motor Sport is the best way to start before moving into Circuit Racing (many of the top racing drivers started in Car Club activities). Similar to Circuit Racing are Regularity Events. They have multiple cars on the circuit, but instead of racing each other, you nominate a time that you can match for a set number of laps.
Motor Racing is very exciting, but need not be overly expensive. Races start at club level, where a vehicle need only be modified to comply with CAMS safety requirements.