For your application, I suggest the 95gr Nosler Ballistic Tips.
I've found that for two rifles I've recently worked with that 41.5gr of IMR4350 was excellent.
However, I'd suggest you start at 39.0 and work up. 41.5gr gives 3,100fps from a 22" bbl. It has an excellent ballistic coefficient (95gr B.T.) and will open up (expand) well at the extended ranges you are shooting at.
My experience with the .243 is that the bullets can fail at close ranges (under 75yds) due to high velocity and fail to expand at extended distances (over 300yds). The ballistic tips are very frangible at close range, but at longish distances perform as they are intended to.
For a close range load, I suggest the 100gr Hornady Interlok (flat base) as it holds together decently. The 100gr boat-tail Hornady isn't an "Interlok", so avoid it for close range shooting. For long range (0ver 100yds) it's "ok". For mule deer, you'll do better with the 100gr Nosler Partiton.
I'm not a huge fan of the .243. I've shot too many deer with a .257 and .223. I'll take a .257, 6.5, or .270 over the .243 any day. And a .22-250 for varmints...... and small deer. The .243 just dosen't "do it" for me.