"Best" bullet is simply the one that is most accurate, and can do the job at hand.
With the velocities that can come from a rifle, avoid JHP's at all cost, save perhaps the Nosler Partition handgun bullet, and any "x" bullet from Barnes.
You won't find them necessary, though - critters with .45 cal holes through them seldom go far.
Personally, I'd start at 300 grain bullets, cast, in either the WFN or LFN profile. Gas checked bullets will probably shorten your load development. If 300 grainers work, great, if not the accuracy you desire (or you can't regulate the sights) then perhaps one bullet weight lighter or one notch heavier. In .45 cal they should all work OK, if in doubt stick with heavier bullets.
If you really want to use jacketed try the Speer 300 grain or Sierra 300 grain. But the cast ones will work for certain and you won't have to worry about them flattening out against bone and failing to penetrate.
Assume you have load data, if not check the latest Hornady, Hodgdon, Speer, etc., etc., for 30,000 CUP loads w/H110 or 296. Jacketed load data should be safe for a quality cast bullet.
For all around versatillity in the .45LC trapper, I'll have to agree that the 300 grain bullets have a great appeal in terms of their flexibility of use and the velocities you'll turn up in that carbine!
Choose any of the profiles, the LFN, WFN or WLN bullets, with gas checks and you'll have excellent venom for anything in North America that you would reasonably hunt with your trapper! Load them with H110/W296 and you'll never look back!
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