I think that everybody here so far is pretty much on track. The only other option I can bring up is steel matches. If there is a club nearby that shoots steel matches, I'd recommend that you try that first.
Don't get me wrong, as my personal favorite is IDPA, but I believe that steel matches are the most readily accessible form of competitive handgun match around for people new to competitive shooting.
Reasoning (and yes, it's a personal opinion) has to do with the simpler format and rules in steel competitions.
Plus, there is that satisfying "spang" when you hit a steel target...
As much as I believe that there is good in every person, I'm not so naive as to think that all people are essentially good. Evil and evil people exist. Deny that fact at your own risk.