Given you are a reloader, I'd too look at the 20 Practical, as just as easy to load, never a brass sourcing problem, etc. The .204 Ruger would be a good cartridge. Won't blow them up like a 22/250, but dead is dead - and it will do that pretty well. For groundhogs, I'd stick to the heavier bullets, like 39 Blitz king and 40 V-Max, though the 32 V-Max is good too, especially for the shots not way out there. Test a few powders to see what your barrel likes, using load data. Accurate LT32, Reloader 7, H322, Varmint H4198, etc. If your rifle has a brake, the .204 is very tame, enabling you to see your hits through the scope, which is nice. There are some good lead-free bullet choices with the lead-free Ballistic tips - and the Varmint Grenades from Barnes. The lead-free are a great choice when shooting farms where ricochets might be a big concern. The sintered metal cores of the lead-free bullets really come apart on contact, making them a safer bullet in that respect, I think. Personally, I think that unless you go with a really fast twist to be able to shoot 50 grain Bergers (when and if they are available), your maximum "effective" range shooting the 40 and 39 grain bullets will be around 350-450 yards. The 50 will push it out more. This is assuming good-shooting rifle, good optics, etc. You can still hit critters further than this - but with the significant velocity loss - you will get a much higher number of wounded, even when well hit.
I like the .204's due to the high-volume shooting I do when hunting (primarily ground squirrels, with some coyotes). I need a barrel to remain cool enough to remain shootable after continuous, long strings of fire. I think if I were shooting ground hogs only - and maybe a coyote or other critter here and there, I'd opt for a larger cartridge with a bit more horsepower, where I could reach much further out - like a 6mm Creedmore, 6BR or something - or just a good 'ol .243. Maybe a .22 Nosler shooting the new eldVt? Something like that would keep with the low recoil and extend range a lot. So many choices!