100gr in 243 is meant for deer and similar, unless its specifically a target bullet.
If you're buying commercial ammo, you'll need to stick to probably close to that to get a big game bullet.
If you "roll your own", there are big ge bullets down to 80gr (Barnes TSX) that are phenomenal. They're available in factory ammo too but have a defibrillator nearby before you look at the price.
For shooting varmints, find something light and fast... 55gr or so. Heavier bullets work fine and buck the wind better at long range but 200 yards isnt long range. I like light/fast.
I would recommend the 257 Roberts, does everything you are looking for. If you reloaded and if you could find a rifle in 6mm Remington, I would also suggest that.
I love my 6.5 Creedmoor, but it is somewhat of an over kill for varmint hunting.