Mach Bike all the way! The Acro bike was cool and all, but there were very few times where it was actually needed, and it usually just lead to some rather uninteresting items. I think it may also be needed to get to the spot where you can catch Feebas, but that's the only thing I really find it useful for. There may be more, but that's not anything I'm really familiar with.
The Mach Bike however is much more useful, just in the fact that it's so fast. It makes travelling a lot faster, and it's necessary to catch Rayquaza, which is pretty much an instant win in my book. I also actually really enjoyed trying to beat my best time on the Cycling Road, so yeah, so many more positive things about the Mach Bike.
As for the first one I picked, I believe it was the Mach Bike, but I honestly can't remember.