Ok, wood or synthetic?
I advocate either one. Makes not one bit of difference if the gun is done right.
Bill Shehane does a good job with his laminates, I've used several during my tenure with Nesika.
The big stocks from McMillan work just as well.
If you call Nesika and ask for Mr. Richard Spruill you may still be able to obtain a "Nesika Varmint" stock made up with a fairly unique laminate called "Fibron."
If you want a stock with some mass, this is the way to go.
I have a 22-250 done up this way and I can literally watch the bullet go down range all the way to the target. Not the trace, I mean the bullet itself. (32X on the bags @ 100 yards in the COR-BON ammunition tunnel.)
They won't be inletted or finish sanded on the outside so it'll take a bit of work to get it done up.
Thats just another option for ya to consider.
What I've learned to do on bag guns is to fiddle with how the action sits in the stock. It's taboo in most circles to orientate the action in any fashion other than dead nuts parallel with the stocks "water line". On bag guns I've taken to the practice of just ever so slightly elevating the muzzle so that the barreled action is essentially "ramping up" and out of the stock as you go towards the crown.
This is a well versed "trick" in bench circles as many feel it aids in how the gun tracks in the bags.
It's so subtle that the casual observer really won't even notice it.
As far as muzzle brakes goes:
I've installed and shot a lot of Vaise brakes. They work well at taming a savage beast. This is what I used on my 22-250, 300-338 Lapua Magnum, and my 338 Lapua Magnum. I have no complaints. If you go this route one word of caution. Be damn sure the person installing it understands how they are made. You go turning the OD past the minimum dimension documented in the instructions and you will "ventilate" the brake and ruin it. The outer holes running parallel to the bore's axis are what I'm talking about.
Experience is never cheap. I'll leave it at that.
I've also designed a brake that is used on the Dakota Arms Scimitar tactical rifle. It's not very exciting as far as brakes go, but it does work well enough. It also helps to reduce (not eliminate) the signature of the gun. Those big boomers create a pretty good dust print.
The brake itself isn't the novelty, its how its made that is pretty cool. The vents are machined with the brake "blank" threaded and torqued onto the barrel. This way you index the barrel in the machine and you know for sure that your clocking is dead nuts. Nothing reeks of "Rookie Night" more to me than a muzzle brake rotated off at some retarded angle.
Anyways. . .
Another thing to consider is having one (or more) slush tubes installed in the back of the stock. They do help to deaden the level of movement in the gun during recoil. Other "tricks" that I've done is to add lead to the forend under the barrel. I once machined a pocket feature and just mixed up lead shot with acra glass and poured it in the pocket and allowed it to cure. Then I finish machined the barrel channel and capped it all off by laminating a couple sheets of carbon fiber twill weave cloth right along the whole length of the forend.
Nothing adds to the "bling" factor quite like carbon. Customers get all giddy over that stuff.
So, there's a few ideas regarding stocks and brakes.
Good luck, hope this helped.
. . .and no, that scope is not touching the barrel /\. I promise!