First thing is to determine what's popular and/or available in your area. Some places (like here in PA) are blessed with pretty active communities (with a lot of cross-over) involved in both the "Practical-Tactical" (IDPA) version of the game and the "Run-and-Gun" (IPSC/USPSA) version.
If you are just starting out and don't have either equipment nor preferences already built up, either game will be a great place to start. Try here for IDPA info:
http://www.coloradoshooting.org/fridpa.htm. Or here:
http://www.uspsa1.org/ to locate USPSA (IPSC) events.
If you own a centerfire handgun that could reasonable be called "defensive", there's a REAL good chance that either sport will have a division into which it would fit. Don't go out and buy anything (including holsters and other gear) until you've gotten your head around some of the equipment rules and tips-and-tricks of whichever sport you think you'll land in.
If at ALL possible, contact the head honcho of the IDPA or USPSA club closest to you and find out when their home crew meets for practices. Visit them on some practice nights and ask to watch what they do and try your hand at it. They can take a look at your gun, holster, mag pouches, etc. and give you some suggestions if you need to tune up your kit. And you'll get the chance to get some of the basics techniques, rules, and terminology down pat before you step up to the starting line "for real" -- and you can meet some folks and get a bit of a support crew to help you through your first match(es). If you just CAN'T get any prior experience/exposure, just show up to a match. Everyone likes to see new shooters getting involved and they'll probably offer to have someone walk you through it.
Now for the gross generalizations:
IN GENERAL, IDPA is going to be easier to get involved in with equipment you probably already have -- and equipment you might use on the street. (Standard "concealment" holsters, basic & secure mag pouches...just a couple, no huge quantities of magazines, etc., street clothes, athletic shoes or hikers, and a concealment vest.)
IN GENERAL, USPSA/IPSC is going to encourage you to purchase more specialized equipment to shave as many thousandths of a second as you can from your times. (Skeletonized rail holsters, vast arrays of mag pouches, lots and LOTS of magazines, baseball cleats, knee pads, etc.)
IN GENERAL, you get to shoot more in USPSA/IPSC. Expect round counts per stage to be averaging at 20 or more, with probably 150-250 rounds expended per match. And you'll load up all the mags you can carry with lots of rounds and reload as often and wherever you want.
IN GENERAL, you'll shoot less in IDPA (round counts per string of fire are limited to 18, but there will be occasional courses of fire as short at 6. And, every once in a while there will be a crazy ONE SHOT stage!) Expect to shoot between 75 and 125 rounds in an average club match (5-7 stages).
IN GENERAL, USPSA/IPSC stages are wide-open, run-and-gun affairs where you're presented with a sea of targets and you blast them as you see them -- and that's about it.
IN GENERAL, IDPA stages will require a bit of strategy because of the emphasis on using cover and because your ammo and your reloads have some limitations designed to simulate what, in theory, might happen in real life. You can't run wantonly through rooms full of targets and pick them off at your leisure. You'll have to engage them in logical sequences determined by the criterion of minimizing your exposure to return fire.
Anyway, a dozen guys will now jump into the discussion to point out lots of ways I've oversimplified the distinctions, or to point out how USPSA is fine tactical training ... and how IDPA
isn't good tactical training, etc., etc....etc.
My point is, go, get involved and find out how much fun IDPA and/or USPSA are! Either one will do to get your feet wet. If you have a choice between local clubs that run both, look over the mission statements of both organizations and their respective match styles and choose which ever one tickles your fancy.
When you do finally get some trigger time remember that the only way you're going to impress anyone is by how
SAFE you are!
Have fun and be safe!
-Sam