I am sure you will get other input, but there are a few things that do need to be answered.
What is your intended goal for your build? Are you going to use it more for hunting or target? Is weight gong to be a factor? What is your budget roughly for putting it all together?(nothign that need be posted but considered)
The 300 WM is capable of launching a decent bullet WAY out there and very accurately, but depending on a lot of variables with the rifle you already have you can spend a bunch of money and still not be happy.
Yes you can strip it back to only the action and start fresh, but if this is your first look into such a rig, I would suggest first and foremost simply bedding the existing stock if it is a good one, or swapping it first. Work up a load for the bullet or weight your wanting to use, and see how it goes from there.
If your looking at ranges from 400 - 800 yards a good 185 - 200gr bullet would probably take care of anything your going to shoot, up to stuff that might want to eat you, and even some of that.
After that you might look into upgrading the optics. Having the trigger worked on if possible, putting a brake on if necessary or desirable. Just small things that might get you some better ideas of where you want to be a little at a time, before dumping 2K into a rig that is only going to sit in the safe, or be sold shortly there after.
Personally I would go the stock route first, and work from there, if this is your first build. If the rifle has a good barrel might as well burn it out first. That way you can learn some of the methods and techniques of hitting the targets WAY out there before spending a lot of hard earned cash. Another thing to consider is how much your actually going to shoot this rig. Will it be once a year or something that you will put several hundred rounds through a month. If the latter, you might consider something a little less appetite for powder. Just simply looking from a financial standpoint.
As was pointed out to me when I started, once you start dumping 80grs of powder or more at a time, you go from #1 cans of powder to #8 jugs really quick. Also once you start looking for the best loads, you do not want to be having to rework your load with every new pound of a different lot of powder, you want the consistency of the bulk jug and more loads per purchase.
Another consideration is magnum primer availability. When using a bunch of powder in a case this size these are almost a must for good ignition of the slow powders that are generally used.
Anyway, just a few things to think over. IT is a hoot however to reach WAY out there and touch something even if all the end result is, is a resounding clang of impacting steel.
Good luck and I hope this helps.