.22 rimfires (.22lr and .22 mag) are for hunting small game, as they don't destroy as much meat, and offer better penetration. They are also good for target shooting.
.17 HMR is for target shooting (primarily, IMO), and destroying small varmints, where you don't care if you save meat, because you won't save much.
Two different purposes. What's YOUR purpose? You didn't say.
.17 Mach 2 - well I'm not so sure there IS a purpose for it. But it's kindof a jack of all trades, pretty good for small game hunting, I guess(not TOO much meat damage, although some), and a little more range than .22lr, but not quite as good as .22 mag for longer range small game hunting, IMO. Pretty good for target shooting, although not as good as .17 Hummer past 50 or 75 yards. Cheaper than .17 hummer, that's for sure.