On the SRT, if you don't fancy a club, my advice would be to find one of the CIC instructors and spend at least some time with them getting it figured out quickly and efficiently. They are not just good at SRT, they are good at teaching it. You are correct that you can't do big trips off the back of a 1 or 2 day course, but you can go and do easy stuff. Then go back to get more knowledge as you need it.
I'm not a member of a caving club, but have built a group of active cavers out of our climbing club. This has how it went for me over the last couple of years :
I'm a climber and tried to sort some of it out myself in a quarry, then had a couple of goes at SRT in a cave with some caving mates, all felt very hard work.
I then spent an evening with Steph & Mike at Yorkshire Dales Guides. That sorted the simple up and down stuff. There is some important stuff here about procedure for checking the point you start to abseil. I'd strongly recommend learning this correct first time, so you always do it like that by muscle memory. Definitely a case of you don't know what you don't know.
I bought the caving techniques and alpine caving books.
Then I could go on simple trips with the cavers in the climbing club, following other folks rigging. After a few trips, started de-rigging. This helps to learn about carrying bags and avoiding tangles.
Then I started rigging in simple caves, with folks who were competent and able to look after themselves.
Then I tried things that were slightly technical and awkward but in a relatively safe location (Yordas chapter house traverse, Jingling Pot traverse and lateral shaft etc.)
I did the CNCC pull-through rigging course. Lots of good stuff in there.
Then I did the CNCC 1 day srt rescue course. That was really useful and gave me a lot more confidence to solve a lot of problems from the pitch head. I changed some kit to give me more options for this.
Over the last few months I'm now in a position where I can rig most of the standard sporting-type trips on resin bolts (Lancaster Hole, Lost Johns, Boxhead, Gavel etc.) and at least have an idea what to do it someone got strung up on a re-belay, too exhausted to jug or lost/broke some gear.
Now at ~60 trips, half or so on SRT. Still lots to learn. It helps to cave with people with more experience to pick up tips. It also helps to start showing/mentoring new folks so you can really consolidate what you know as you pass it on.