I have more experience in this realm than I do precision rifle so I'm glad I can actually contribute!
I shot IDPA/USPSA with a Glock 34 for about 5 years. I competed in Production/SSP (respectively) so the modifications were simple and overall my "competition" gun was under $1000. The best thing about Glock is their simplicity and reliability compared to other platforms. Some are going to contradict or maybe even get bent outta shape, but all the matches I've shot and seen stoppages/malfunctions, slim to none were Glocks. The Glock 34 shoots softer (less muzzle rise/flip) than the Glock 17. That's with Asym Ammunition or Speer 147gr, but I can easily notice a difference. My splits don't lie and they are quicker with the 34.
I dabbled with the M&P series prior to Glock and had no issues, I switched only because I got hired with a new department and they issue Glocks. I wanted platform consistency and switched to a 34 since I'm issued a 17. I will say the Glock trigger is better out of the box but everyone switches them in either platform and I've never fired a custom M&P one. BUT, I swear by the Glocktriggers.com edge trigger. I used a lightweight STEEL striker combined with 4lb firing pin spring and with ASYM 147gr never experienced a light strike in two years (about 4000rds).
All that being said, I recently switched to a CZ SP01. It shoots very flat and recoil is basically a thing of the past. I dislike the sa/da compared to striker but I think it's because it feels so new. The biggest issue is the complexity of the firearm. I'm a 1911 fanboy and I can't believe the CZ is more complicated than a 1911 in that regard. Glock, I can have the entire thing completely disassembled in one minute with one punch. The CZ requires a myriad of tools and is very complicated. I haven't had any reliability issues but I've heard its more finicky in regards to spring weights and ammo. I only shot one major match with the CZ and I did shitty but it was because I performed very inconsistent. I'm going to give it another shot this season and see how it does. It's weird, it's flatter and softer than a Glock but it's harder to shoot. In other words while it can perform better, it's harder to achieve those results. The Glock 34 was just easy to shoot and was more forgiving in regards to driving it fast. The CZ is like an on/off switch, you either do great with it or it's harder to shoot well.
In closing, if you are just starting out go with an M&P or Glock. They are pretty interchangeable and have similar recipes to be competitive. Just get which ever feels best in your hands!