The 226 is just fine; I have shot the following in IDPA (each was/is my carry gun at the time):
1) 226 .40
2) 228
3) G19 (current).
I have been at it for about four years and am currently shooting even with the Expert class in SSP using the G19, IWB holster, and a single extra mag carrier, with an untucked button down shirt. So, you can be somewhat competetive even with a very real-world carry setup. I wear my setup to the match, and then out to eat afterward.
That said, once you have been at it for a while, if you want to make Master you will want good dedicated gear specifically for IDPA, but that is down the line and there is no reason to try to start there. As others have said you can get a great feel for it, and reps with your real world carry gear using what you already have. Just make sure you *do* bring the full gear list mentioned earlier... if you don't, you will not be able to shoot:
1) Pistol that fits into one of the classes. Details in the rulebook.
2) Strong side belt mounted holster, IWB or OWB is fine. No pocket holster/drop thigh/cross draw/etc will be allowed.
3) Eye/ear pro...
4) Cover garment that conceals your entire setup when your arms are at your sides.
5) Weak side mag carrier (I don't think this is absolutely required, but highly recommended)
IDPA is currently the most fun I have shooting, period.