I might be able to shed a little light for you. I've hunted with a .223 T/C for 38 years. Taken 1118 groundhogs with it and several deer.
First, you'll probably do a little better with 50 gr. bullets-flatter trajectory, more speed, better terminal performance.
Second, scope. I've used a Burris 3-12 since they've been out. Best long range scope available for handguns.
Third, sight in. I have mine 2 1/2" high at 100 yards (as all of my single shots). This puts you about dead on at 250, 1/2" up at 25, 1 1/2" at 50. By doing this you're on a groundhog size animal to 300 without holdover.
Fourth, bullets. For varmits, BTip or VMax. I use Hornady SXs a lot. They won't exit. For deer BTs and 45 gr. Barnes X do good.
Friends and I have done groundhogs out to 400 yards. None ewver moved.
This is an excellent low recoil varmint round.