The Kempston joysticks had autofire and multiple triggers and fire buttons. Thing is the off brand ones my parents used to buy me probably werent the best quality and didnt really make it through too many sessions of Daley Thompsons Decathlon, or Carl Lewis Challenge. That Atari joystick was a tank and I wont hear a bad word said about it!The C64 used Atari-style joysticks, too. They had the same connector. Any Atari joystick would work with it, but you could also get 3rd party ones that were a lot better than those piece of crap Atari ones.
I had a few games where you had to push the joystick button as fast as you could to go faster. I ended up trying to cheat by buying a joystick that had a rapid auto-fire switch. Unfortunately, it was slightly slower than what I could do manually.