ORIGINAL: Folically Challenged
'Tis my understanding that the '06 won't push most cup & core bullets so fast that they'll come apart, so a "standard" 165 to 180 bullet oughta do fine for moose & deer. You can try Corelokts, Power Points, or Hot Cors, & see what your riflelikes best.
FC
I've seen std. 165's loose there cores on bigger animials numerous times, and if 165's are going to be used on moose, i'd go with a premium bullet to get more penetration. OR, go with 180's in a std. bullet...
DM