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Funny, few folks would think of using a .308 for a varmint rifle, but it will certainly work.
I have and I've used mine for bait shooting some this year. Mine is the ultralight version.
I make some routine mods {as noted in a couple other threads} to Rugers as SOP when I buy one, so maybe I am not the one to ask, but mine "after" is sub-MOA with several bullets. Mostly I use 150 Speer SP's though it shoots 147 FMJ's and 220 Hornady's into an inch at 100 meters/109 yards also.
{As to the last bullet, remember, Ruger .308's have a 1/10 twist. Kudos to Ruger for that! So you are not limited to shorter bullets as is the case with most standard rifled 1/12 .308's. The 220's make for an interesting load, duplicating the old .303/215 grain load from a short action short barrel rifle.}
Anyway, for varmints, the 150's will work, but remember, you will typically not get the spectacular explosive results that the centerfire .22's and other highspeed rounds will produce.
Here's a Columbia Ground Squirrel shot at about 90 yards;
Shot similarly with my "varmint" rifle, a Ruger MKII .270 loaded with Hornady 100's running 3560 fps, results are usually more dramatic. For bait shooting, I prefer the .308 w/ 150's and 6.5 Swede with 140 SP's as there is more left for the bait bucket. The .270 with the light fast bullet tends to scatter parts.
But for groundhogs, you might find the .308/150's let them get away to the hole before dying. Many years ago I lived in Kentucky and shot groundhogs with a .30-06 on the farms I worked on and found the 130 Speer HP at top speeds was a good stopper whereas some 150's and 180's would not open up fast enough to kill them at the shot. So for ghogs I think I'd go with 125-130 grain bullets, max speeds and keep shots under 250 yards. Just my $.02.