I enjoy
USPSA the most for sanctioned events. My reasons are basically the same as Alpha Sierra.
Planning each stage from start to finish can be a challenge in itself. The high round count draw and shoot field stages are my favs.
The huge mix of moving, disappearing and stationary target-types is a big part of the fun.
Steel Challenge IS a great way to develop accuracy and speed, but isn't as much "Fun" for me. It's a more rigid discipline that gets repetitious to me after a few stages.
Lots of steel (20 +) of various types and with shooter movement IS a lot of fun for me. Plate racks, poppers, falling plates, fixed plates, triangles, the Star, bowling pins, rectangles, and many more make for an adrenalin rush when the buzzer goes off.

An old-time carnival comes to mind.
Like JoeL always says, "This is fun, but this isn't easy"
Local shoots can be a lot of fun too. Steve Bonnet, previous National and International champion shooter, sets up a "Fun Shoot" here every week at two different local gun ranges. He sets up 5 stages that mix ALL THE ABOVE together using
a blend of USPSA/Steel Challenge and IDPA rules. On 5th Saturdays it's a three-gun event Rifle, Shotgun (

) and handgun---even .22. He often has a BUG stage and/or a rifle stage that can be shot with handguns if preferred.
Waaay fun to shoot.
For those who have thought about going to a handgun event, no matter what type, GO. You won't be sorry, and you will smile. Take what you have to shoot and GO. You'll learn more/faster here than you will any other way. New shooters gain more than anyone else and are always welcome and helped.