The common old bonded core Woodleigh 180 or 200gr Protected Point bullets would be the first ones I reached for, and I doubt very much I would have to look any further.

Except they aren't commonly available where I Live. More's the shame.

markb, You have achieved overload yet again!!!!

You know what they say about opinions. The which is best question will stir it up every time. There are valid points made for the many different offerings.

Point is you're asking for a bullet that will cover a big velocity span, used in a mag for deer sized game. The 300 WM up close will make a mess if the frontal dia of the bullet gets big quick so the advice to use X bullets is good. At longer ranges and lower velocities the rapidly expanding bullets work good.

Keep in mind the animal size. Your rifle will be fine with most bullets. Pick a bullet based on what is the most common shot. Knowing how the bullet will work up close or at long range should determine where you aim. If the bullet you choose is "soft" then shooting into the shoulders up close is foolish, where the same bullet will go through the shoulders at long range. As always shot placement is the most important factor! Even the "cheap" standard bullets will work when used within the design specs.

Most real failures you read about I believe are the result of using a bullet outside its design window. ie: light, thin jacketed bullet going really fast out of a mag because the velocity #'s look good. OR really heavy, stiff bullets not going fast enough! The ballistic tips, sst, sierra, core-loc, interlock, ect. are great at standard velocities. A standard bullet out of a mag at long range will perform the same as a '06 with the same bullet at closer range.
I have had complete pass throughs with the reportedly fragile Sierra Gameking on Mule deer. Knowing the bullet and considering the situation should determine shot placement. Are you jumping them out of their beds? Stalking? Most shots at deer are well inside the 100 yard mark for the majority of hunters. For that reason, and the size of the case you've chosen, a heavier bullet or a stiff construction bullet would probably be the best choice.

More practice is the best way to improve bullet performance at long range!

Notice above I said REAL failure. Most of the stuff you read that turns to trash talking is grossly exagurated. This internet thing can be a great way to gather info. but can also start to bring discredit when it's undeserved.