Ditto. I'm a big fan of the .17 Hummer. Never had a .17 Mach 2, so cannot comment, but people seem to like them also for the cheaper ammo and good effect.
I've owned 5 different .17 Hummers and still own 2 of them. They are a hootenanny - easy to make hits to 100 yards even with wind. Without much wind, easy to make hits on squirrel-sized targets to 125 or so yards. Accurate & fun. Virtually no recoil, and little noise - what's not to like?
On the .223, the range is gonna depend on the wind level, your skill, the ammo selection, your rifle's accuracy; everything. But if everything comes together, you should be able to hit small rodent-sized targets out to 300 yards or maybe a smidge more with the .223. With the .22-250, again with ammo tuned to your gun (good handloads), etc., you can extend that effective range to 350 yards or a bit more if everything lines up. Now sure you could occasionally make lucky hits to 500 or even 600 yards, but to consistently have a better-than-even chance of making a hit, you're maxing out around 350 or so, in low-ish wind. Of course, lots and lots of practice can improve that some. You are going to reload, right? If you are not, then you definitely want the .223 rem as a long-range varminter choice, to have a good factory ammo selection. Realistically, when there is wind and an average skill level (such as I have), then .223 is effectively around a 250 yard gun for small targets like that, as Mr. NCsmitty says, and the .22-250 or .220 swift around 300.