My barrel is a 1/38 T so anything over ~0.850" shoots patterns...3-5".
So far I've tried 180 gr Rems...hi velo, little recoil but probably would grenade in any good sized animal...240 gr jacketed - excellent choice for deer for higher velo, good accruacy and original 444 M bullet weight...265 gr Hornady - best accuracy, excellent velocity, one of my favs...265 BT LFNGC cast...didn't do as well as I wanted accuracy wise, but OK hunting accuracy...300 gr Horn XTP - very good velocity, accuracy 1 3/4" at 100, slightly less energy at 100 than the 265 Horn...270 Speer Gold Dot - 3/4" groups at 100, high velocity and energy at 100 yds and toss-up between it and the 265 Horn...310 BT WFNGC - I liked this bullet but the rifle didn't, patterns and some sideways hits on paper, definitely not stabilized. I tried H4189, H4895, Benchmark, RL10, 8208, RL-7 AA2015, H322 and H335. Ran out of AA2015 before getting anything good - RL-7 very good as was H4198.
Read the information on Beartooth on the 444...lots of very good stuff there.
I have 3-400 different weight bullets to use up on sageratz and other varmints, but I will probably only use the 265 Horn JFP, 270 Speer GD and 300 Horn XTP for deer and maybe elk...and the 450M BLR/450M Marlin switch barrel with 350 Horn JFP or 400 gr jacketed something for the bigger game...and I use 430 gr TrueShot and 450 gr BT in my 458 American SMLE.
Of course if T-RexSageRat happens to show up on the wrong side of the fence I have some 720 gr 45-120's just waiting. Hahahahaha
For a 1/20 T barrel you probably will have a hard time besting the Hornady Lever----stuff, but it won't shoot in my 1/38 T.
I have large caliber rifle to do one thing...shoot heavy bullets at BIG animals...doesn't matter one whit if I could kill it just as dead with my 6.5 Swede or probably with my 243 with a solid bullet...it's the principle of the thing...big goes with big...big guns, big game, big dogs, big engines...BIG TRUCKS...
My only problem is I have to grow a little more to get into the BigBoy club...
Luck