As far as I know, IDPA matches are either pistol-only, or 3-gun (pistol, rifle and shotgun), though they may have side matches at some events. The same is true, I think, for USPSA.
The real question is whether you are just looking for some competitions to hone your skills or whether you want to get ranked and compete at a national level. There's nothing wrong with both, BTW.
What I would do (and we all know what one person's opinion is worth) is look around at ranges in your area. Check out their websites. If they are like the ranges around me, they will have a section on competitions. The reason I would do that instead of going through the organizational (i.e., IDPA, USPSA) websites is that some ranges hold non-sanctioned competitions.
In my area, for example, an fairly new range started hosting "action pistol" competitions. They used USPSA/IPSC targets, rules and scoring, but they didn't use the name because they weren't a sanctioned club. Now they are sanctioned, so they host USPSA matches. But they also kept up the non-sanctioned event and began a rotation of pistol one month, carbine the next, then pistol and carbine combined.
Once you know what's available in your area, you can decide what's best for you. The range will also likely have contact information for every discipline they host. You can then find out more about the local matches. In my case, my decision was to shoot Steel Challenge because I work a lot of Saturdays and the IDPA and USPSA matches are on Saturdays, while the Steel Challenge matches are on Sundays.
Once you find something you like, you can decide if you want to concentrate on one organization, travel a bit farther, etc.
Hope this helps.
"An armed society is a polite society." — Robert A. Heinlein
"After a shooting spree, they always want to take the guns away from the people who didn't do it. I sure as hell wouldn't want to live in a society where the only people allowed guns are the police and the military."
— William S. Burroughs