For a revolver, I would get a medium weight JHP or JSP. One member posted 180 gr bear loads, they may work but a hard cast through a deer wont do much damage. May work for some guys but I shy away from them for deer. I do limit my shots with handguns to 30 yards and closer with iron sights.
I personally load 158 gr XTP for my 4" Smith and Wesson and have had great performance from it. I have some of the FTX bullets loaded in the LeverEvolution ammo but I have heard mixed performance on that.
If shopping factory, I know Grizzly Ammunition loads 158 gr XTP and uses either Jagemann (JAG) or Starline brass. Both are excellent and I would not hesitate to buy that ammo.
Likewise, I believe Buffalo Bore also loads 158 gr XTP which out of a 6" should do very well with a good mix of expansion and penetration
Stay away from cheap JSP ammo like the Remington 125 or 158 gr. The bullet is poorly designed and made in a way that the bullet overexpands and basically spalds outward as if it hit steel from the hydrostatic forces. Ive tested it in both .44 and .357, and both failed.
If you cannot find XTP factory ammo, I would try Barnes or Norma. The Silver Tips from Winchester seem to be inconsistent with expansion IME