A Glock 19
For starters I'd suggest you get a pistol that has the same trigger action on each shot. You have enough to deal with right now - you can learn to shoot a SA/DA later if you want.
So, your choices could be as simple as an XD, Glock, 1911, or a revolver. I'd suggest you buy a pistol that fires cheap ammo and has a good selection of holsters and accessories.
The XD in 9mm would be a great choice although you might not be competitive in contests right away. Still a good choice for PDW. Remember, IDPA's rules only apply at their matches.
Revolvers, while excellent weapons, probably wouldn't satisfy you right now.
1911's are great pistols but are best in their original 45acp, which is expensive relative to 9mm, and in 9mm form can be finicky. In any caliber they're expensive, either up front or after mods. Get a good 1911 when you're ready to shoot 45's. Then consider reloading too.
That leaves Glocks. My suggestion would be either the model 17 or 19. Ammo is cheap, holsters cheap and abundant, ditto for magazines. If I HAD to choose it would be a Model 19.
That said, I shoot a 45acp 1911, never won much at big matches, but I have been playing IDPA for a long time and I have seen many new shooters and introduced quite a few new shooters to shooting and to IDPA.
YMMV. Just my 2 cents. For free!
jeff