I'd go for a GTI. The Mazda is a decent car as far as I know, but I've never owned one so I don't have much personal experience to base it on. I don't know much about the Hyundai Veloster. I saw it and knew I could never buy one because of the way the back of the car is styled... I think it's hideous, but that's just my opinion.
I've had a 2003 Golf (not a GTI
) for over 3 years. I think the only thing that would make my car better would be if it were faster, and that's what a GTI is all about. Same reliability and practicality, but more fun (and maybe slightly lower fuel economy but still not bad) If you went for a GTI, I doubt you would regret it.