I got into competition shooting to build my pistol skills. With an old S&W 910 and a crummy leather holster I managed to place in my division in both State and Regional USPSA competitions in the early 2000s.
I am a Chief Range Officer in the USPSA organization, which means that I am trained in both designing and running courses of fire.
USPSA and IDPA are the two largest competition pistol organizations and you can find a match near you just about every month if not every week. You will typically find an open and accepting community of pistol enthusiasts.
I think both disciplines offer good challenges and opportunities to build your skills. I prefer IDPA as it has more focus on use of cover, engaging in tactical order, and ammunition management.