Take your pick 150-180 will work fine with 06 & whitetails. Being you don't expect to shoot further than 200 yards I'd probably lean to the 165-180 side of things, as you really don't need to worry about longer range shots and trajectory gains of 150 gr bullet. I'd also personally pick a flat based bullet vs a boattail, sono need for a polymer tip or bonded either unless you just want to try one. Something like a hornady interlock sp, nosler partion.etc in 165 or 180 would be about perfect.

Good luck