MOST conventional hunting bullets will reach and take out vitals on deer w/ no problem at sane ranges.
No deer can survive a good 24 cal bullet or larger IMHO when placed well, (again 'hunting/game' bullets, not varmint bullets).
Even 22 cal w/good bullets do deer in fine at your 200 yds and under mark.
Shoot well, and everything else usually takes care of itself IME.
