I get a kick out of these posts. They seem to be popping up alot lately. What the BEST for this or that.
In all honesty, you are the best part of the rifle for long range hunting. There are 500 chamberings that would work and be fully capable of taking deer and coyotes at long range in a short action Rem 700.
Ballistically, a 260 Remington will nearly match the 300 WSM
as far as ballistic performance and would have 1/3 the recoil.
Some have said many of the rounds recommended are to long for the Rem 700 short action. Again, bunk, its a 20 minute job to install a 3.000" Wyatts extended mag box and then you can use any of the WSM if you want to and even the 284 class chamberings.
The 6.5x47 is a decent chambering but its developing a reputation of having alot of vertical stringing at longer ranges because in my opinion, the case capacity is to large for small rifle primers. It CAN NOT be loaded anywhere near 6.5-284 performance levels unless the first is overloaded and the second is under loaded. Thats just a silly comment.
For what you want to hunt, you do not need alot of bullet weight so unless you want to reuse the factory barrel, I would never recommend a 30 cal for what your using the rifle for. 6.5mm and 7mm would offer better ballistics all around. Even if you dropped down to the 260 Rem or 7mm-08, you would gain ballistic performance, not give up much in barrel life either and have less recoil.
If you want to rev up the ballistic performance, Look at the 6.5-284 or even the old 284 Win which actually is a great short action chambering. Just have your reciever converted to use the 3" wyatts mag box.
If you want more then this, the 6.5mm WSM is an amazing long range chambering for your class of game. The 7mm WSM
is also outstanding, again, you will want the 3" mag box.
In the end, no matter what you have, it is you that will determine if the rifle is effective at long range, that is if the rifle is up to the challange from the beginning.
One thing to consider however is that when you convert a standard receiver to use the WSM, its not as easy at it may sound. Some receivers need alot of tweaking to get them to feed well. Its often not just as easy as opening up the bolt face and your off. That is why you may be much better off with the 08 siblings of the 284 family of chamberings.