I can speak for IDPA since I'm a safety officer, don't know enough on USPSA to comment there.
The Glock 34 and 17 will fit both SSP and ESP. The Springfield fits under ESP, if it was a .45 it would also fit CDP. I don't know much about CZ but I assume it would be ESP.
Here's a quick rundown of the common IDPA classes:
SSP or Stock Service Pistol: Most shooters fall into this category. It's designed for full-size duty pistols 9mm or greater, striker-fired or DA/SA. Division capacity is 10 rounds.
ESP or Enhanced Service Pistol: Same as SSP, but allows for single-action designs and I believe is a bit looser on what modifications can be done. Division capacity is 10 rounds. Any SSP firearm is legal for ESP. Non-.45 1911's fall into this category.
CCP or Concealed Carry Pistol: Designed for compact pistols such as the G26, G43, Ruger LC9, S&W Shield, etc. Division capacity is 8 rounds.
CDP or Custom Defensive Pistol: Essentially the 1911 division, but this division requires the pistol to be a .45. So .45 1911's, full-sized .45's, etc. Division capacity is 8 rounds I believe.
There is also a revolver division but hardly anyone around here shoots revolvers in IDPA for various reasons, and there is also BUG (back-up gun) but that category is not available except for dedicated BUG matches.