As stated above, a deer shot thru the shoulders (which would usually break same shoulders) would have a very hard time running off any distance. I can understand shooting dangerous game thru the shoulders, but never a deer. It ruins too much meat. Regarding your bullets for the 06, try a 165 gr Winchester Ballistic Tip (or the 168gr I always use). The BT is an excellent bullet and will kill a deer every time if you shoot it thru the lungs. Perhaps you might consider getting some of the ammo manufacturers brochures which are readily available from some sporting goods stores. In those you will find ballistic tables, which tell you what type of game specific bullets are designed for and their velocity and energy stats. Using these table, you can decide on 2 or 3 types you want to test. You should try several types to find the brand and weight YOUR rifle shoots the best. There are many great bullets on the market designed specifically for deer sized game and perhaps others will come on and offer their preferences. The 06 is a great caliber and it will do wonderful things provided you do your part.
Good Hunting,
Hal