There are soo many types of cycling clubs out there.

Hardcore racing every weekend clubs
Non-organized large bunch groups of pain in the A*** groups
Touring groups- these tend to go pretty slow for me.

The best club I have joined was a vetrens cycle club- meaning over 30s and mostly older 50+ men and women who wanted to go for medium to long rides in various speed groups, have a coffee afterwards and do the occasional fun race every second month. A nice balance between giving you a challenge to get better (you moved up speed groups etc) but enough social (we chatted whilke riding and had lunch etc afterwards). Organized with over 30 different routes which changed weekly, with help to build up for certain cycling events (like a 160km ride in November most of the club went to).

I miss these guys so much and have made lifelong friends too. We also did Xmas parties and dinners as part of the club. Really good. Everyone so supportive and no one had anything to prove. We even had a 90 year old riding an ancient bike come out every week (the club brought him a new bike for his 90th birthday. He was so happy). Such inspirationation people.