There are, I believe, 3 bullet weights out there-15.5gr NTX, 17gr. ballistic tips, and 20gr HPs. However, what you "should" use is what the gun shoots most accurately, which probably is NOT the 15.5gr. Having shot plenty of groundhogs with 17HMR, it's head shots you want, and limit the range to 100-125 yards. I recommend the heaviest, 20gr HPs if they all shoot equally-well.
The advice I want to give is this-use something with more power. I don't believe 17HMR is a great (or even "good") caliber for groundhogs. When I first started hunting them, that's what I used. My gun shot 17gr. BTs best and on a pressured farm, you couldn't usually get closer than 100+ yards away. Yes, it will do the job but even on smaller groundhogs, a body shot was not a guarantee they're dropping on the spot. Which is the goal of course. I moved up to 22WMR, in spite of the accuracy limitations, and @ 100-125 yards...it was a far more successful/consistent choice. I know the following is likely to be hammered down by the CGN experts, but I also know people will boast about ANYTHING short of stern words being effective at knocking them down. I've read people saying slingshots, pellet guns, 22s, etc. All possible I suppose..under the right circumstances, but you'd be VERY VERY poorly equipped, in the spots I hunt them, with anything that isn't a centerfire.
What IS the best choice? I don't suggest anything lighter than 22WMR for the job, but I've found that 17 Hornet is the best choice of low report, rimfire-like recoil, enough power to drop them on the spot to at least 200 yards (furthest hit I've made with 17H), etc. 223 is probably a more economical choice, and the rifle options are nearly endless in that caliber. I personally use a 204R=more than you need @ 100 yards, but no groundhog inside of 300 yards is safe. (longest shot I've taken with it) Very flat shooting, and enough spice to get the job done probably beyond that.