Most of the competition you'll commonly have the opportunity to participate in these days will be USPSA and IDPA. A Glock 17 or 34 will be very competitive in either.
Don't worry too much about modifications. You're new to the scene and will have plenty of room for development and improvement as you learn the sport and work on your gun-handling, before you need to concern yourself over what modifications might shave the last few tenths and hundredths off your time.
As 56Hawk said, there are several different divisions in each version of the "Practical/Action" shooting sports and a 9mm Glock fits into several of them, depending on what mods you eventually decide to do. With a basic un- (or "lightly-") modified gun you'll shoot in "Stock Service Pistol" in IDPA and in "Production" in USPSA.
I'd hold off making changes until you've got at least 10,000 rds. downrange in competition. By then you'll have a much more developed skill set, and you'll be familiar enough with the tweaks people use to decide for yourself what might make things easier and faster for you.