Wow, I'm not going to tell you not to get one, but that seems like a bit much for coon hunting! My step dad was an avid coon hunter and all he used was a beat up single shot bolt action with .22 shorts.
A 17hmr is pretty distructive for something you want to keep the pelt on, though maybe not too bad on something the size of a coon, they are pretty big, at least around here. Then there is the price of the ammo, do you wan't to spend 8-10 bucks a box on coon hunting shells? For that you could get enough shorts to last your hunting career

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The 17 is more of a long range rimfire varmint gun. Using it for coon would not use any of its positive attributes that make it so popular. Unless you are shooting them off the ground at longer distances? Around here we shoot them out of trees at night. The challenge is finding them, not shooting them.
If you do get a 17HMR I would use the 20 grn XTP's, they are less distructive. And I would look at something like a savage or marlin with the plastic stock and sporter barrel. That way it will be light and cheap.
Good luck,
Paul