I found autoX quite enjoyable. I've done a few track days and I found circuit driving somewhat boring, taking the same corners over and over, compared to autoX where the courses are different every time.

I think it's more a matter of racing getting into you. For me it started with tricycles, bicycles, soap box, dirt bikes, autocross
Saturday night short track NASCAR, Vintage followed by two seasons 1/8 mile dirt LTO Karts. That covers the first 52 years.
The last 18 I have built for and supported other's racing dream.

A friend recently passed, after retiring he started visiting the local indoor kart track. Once he held the track record he took
professional driver schools and when he felt he was ready he bought a race car. He left his wife with over 1/4 million in cars 
trailers truck and spares. I think she has one super track day car with spares not sure it includes trailer. $65,000. Steve (CTR)

It really is dependent on your budget. If you drove a porsche GT3 car, that means you have way more play money than I do. Look for either car rental opportunities that will allow you to continue with HPDE (High Performance Driver Experience) or some other driving academies like Skip Barber and the like. If you talk to the people who run the tracks that you are most interested in attending, they can often tell you who is renting the track on a given weekend and then you can contact that outfit running their event and tell them what you're looking for and ask how you can get involved in their events.

Lots of enthusiast webites out there with forums.

I'm on the super budget end of wheel-to-wheel racing, so I do 24 Hours of Lemons but there are other organizations for entry level racing (no real license required) like Lucky Dog Racing League and Chump Car (aka Champ Car) and WRL World Racing League. You can jump on someone's team as a guest driver by joining their online forum and asking who has a seat available for rent in an upcoming race.

Some groups offer annual racing certification classes like VARA Vintage Auto Racing Association that included classroom and track time. HSR Historic Sportscar Racing has something similar I believe, and I think so do the Spec racing series like Spec Miata. Some of those organizations have a means to do "arrive and drive", which is you pay your $ and someone else takes care of preparing a car and bringing it to the track for you and maintaining it through the weekend.

Really, it only takes $ and ambition. If you have a lot of both, you should find it very easy to get more track racing time. If you are low on either, it will take more time, but still achievable.