lazylabs is right, the 300RUM loaded with 210grain bullets going 2800fps carries sufficient energy to kill an elk at 800 yards. If you can push the the bullet at 3000fps, then you can kill an elk at ~1k yards. So before you go down the road of swapping your barrel, determine whether or not your current rifle is sufficiently accurate enough and whether its exterior ballistics are able to take an elk at the range you wish.
If the answer to both of these questions is no, then rebarreling to 338Edge is a good alternative. It is as simple as rebarreling which you can have done for ~$600.
lazylabs is also right though, that with your rebarreling you will probably want to have some additional work done at the same time. This would bring your cost to ~$1kilobuck (love that term!).
For more specifics on your rebarrel job....
Barrel Length: 28 to 32 (a non-shooting consideration here is getting the rifle to fit in a case. 28" of barrel is about the most you will get in a 'regular' case)
Twist Rate: 1:10 as this will stabilize the 300grain bullets
: personally, I like the Muscle Brake from Center Shot Rifles Center Shot Rifles - Products / Sales - Muzzle Brakes
. There are other good brakes from Defensive Edge, Fat Bastard, Pain Killer
What do you gain by converting from 300RUM to 338Edge: more energy downrange and less wind deflection. You can easily see the differences in exertior ballistics by using JBM's online calculators at JBM - Calculations
Stock: depends on the use for the rifle. If you intend to carry the gun, the more 'traditional' style stocks will work nicely (HS Precision is a good stock). If you are planning on a dedicated longrange/prone rig, I would ecourage you to look at McMillan A5, A3; Manners T2. These are top of the line stocks. If you are a bit more $$ sensitive, look at Bell & Carlson and laminates at Stocky's New Rifle Stocks - America's Gunstock Specialist!
As a point of comparison, here's my 300RUM that is a dedicated longrange rig:
My 300RUM by MCR