A Glock is not a bad choice. If you take reasonable care of it, it should go bang every time. My wife loves her G26.
I'm not personally a fan, Glocks just don't "do it" for me. But that's why there's choice in the marketplace. I picked up a Sig P320 last year, and there's no turning back. The trigger feels a thousand percent better (to me) than the trigger on the wife's glock, and is still much better than the Springfield XDM I used to carry.
I won't get rid of the XDM - I liken shooting that to a big, comfy chair, just with the way the gun rolls with the recoil. I should probably put a trigger upgrade in it.
With modern handguns, you almost can't go wrong. Smith M&P, Glock, Springfield XD/XDM, Sig P320, Beretta PX4, you name it. We're in a great market with lots of fine firearms available.
Concealing something with a full-size frame is a bit more challenging than others. My P320 is a full size, and I've been playing around with holsters, but I've kind of settled on a Safariland OWB and just open carrying most of the time. Here in MO, I can do that with my CCW (CHL). When I need to conceal, I just put a cover shirt on and just sort of half-***** it for a bit. If I need to be more certain I'm concealing, I'll break out my XDM or even my XDS and an IWB holster. Smaller guns are just easier to hide. I do try to plan my wardrobe around concealing, so nothing fits if I have to leave my gun at home