Learn a little bit more about the shooting federations here and what the challenge of each sport focuses on. The rules of each sport are not a focus of this as they can change a lot for each these feds, so I'll leave a link to the latest rulebooks at the bottom of each page.
USPSA is the biggest shooting federation in the US and has some of the most skilled competitors which enhance the challenge and depth of each match. This is my personal favorite format to shoot and one that I think everyone can learn the most from when it comes to pure shooting skill.
Here are some of my thoughts:
USPSA uses what is called hit factor or points per second scoring and this is your score divided by the time that it took to complete a stage. The higher the hit factor, the more points per second that you got and therefore the better you did. The competitors with the highest hit factor on a stage wins. This scoring is a great balance of speed and accuracy with speed being slightly favored.
My favorite aspect of USPSA is the challenge that the stages pose: they're a puzzle, and its incumbent on each competitor to figure out where to go and shoot. This will challenge you to come up with an efficient plan, memorize it, and then execute it on demand; the difficulty of this can not be overstated.
USPSA is a popular and well established federation with a lot of history, chances are there is a match happening somewhere near you. If you have the opportunity to shoot a USPSA match you should take it without hesitation.