Sorry, Have not owned, handled or shot a Henry Long Ranger, so cannot comment on them.
Have owned a few BLR's and I love my pre-81 in 358 Win!
Yes, it has a terrible trigger, but I have shot it lots and know exactly where and when it will break, and produces 1" groups, so I am happy, as I know the gunsmith cannot do anymore to make it better.
Depending on your intended game, any of the cartridges you mentioned will perform well on big game, with good bullets, proper placement and reasonable expectations (i.e. don't pack the 7mm-08 for brown bears at long range! LOL)
Many like the pistol grip (PG) model. Myself, I prefer the straight grip models.
startingto plan on a switchbarrel BLR in the straight grip T/D,with barrels in 250 Savage, 338 Federal and 375 Raptor. Have gunsmith pricing/sourcing the T/D mechanisms for project now.