If you have enough twist to stabilize them, the 107 Sierra has done well for me on antelope this year. If your rifle does not like the 107 then I would try the 85 Sierra Game King as they have served me very well in the past.
I don't own a 243 but I loaded bullets for one for a friend of mine. We chose H4350 and 95 Btip. He killed 2 pronghorn, 2 Kansas whitetails, and a Colorado muley with these loads. Then, he and his wife took it to New Brunswick and they killed 2 or 3 black bears over bait with it. No failures, just dead animals.
I would recomend the 80 to 90 grain bullets because of velocity and twist rates of most
I personally think the 243 is a little light for the traditional chest shot if you don't wan't/like
to track them. how ever, if you shoot them in the neck it is an excellent cartrige for deer
and will drop them in there tracks.
I have seen a lot of deer killed with the 243 and the neck shot is the one I recomend
based on past results.
Use a bonded core bullet like the Accubond and you will not be dissapointed.
The 243 is more than accurate enough for this type of shooting.
I know people that traditionally shoot them in the chest and have good luck,but I still
recomend the neck shot with the 243.
The 85 grain TSX works great for the wife every year, I have yet to find one in any of the deer she has shot. I have a buddy who only hunts with a .243 and has killed 10 moose with it, he waits for them to step forward and drills them through the ribs just behind the leg/shoulder. Shot placement is key.
Berger is now offering a 87 gr VLD in 6mm that bears looking at. Especially in factory twist barrels. I've had excellent results on whitetails with the "hunting" VLDs in several calibers and can't see why it won't be true of Walt's new offering.
Let's get the US out of the UN and the UN out of the US !!