barrowsr,
If you are going to build a rifle for the pure enjoyment of target shooting, trying to tinker with loads, and then maybe break out into varminting or even informal competition,I know you said you were looking to compete, but eventually the draw to compete may be there) I offer humbly to look into the 6mmbr.
Readily available quality brass, TONS of information on loads, many excellent bullets to choose from, decent barrel life, no fireforming, no neck turn option when you rebarrel, and you won't have to change the bolt face on that .22-250, and as accurate as you could want it to be.
If you are planning on having that action 'accurized',bolt trued, lugs lapped, etc...) you may end up spending a bit trying to get it to the level of a custom action like a predator.
I went down the road that you are traveling a few years back, and I wish that I had listened to those who said 'Buy the best you can afford, and cry once'.
If you know you like to shoot tiny groups, you would not go wrong perusing 'the list' and trying to find a good used custom varmint gun. Doesn't have to be a $3,000 uber rifle, but some of the live varmint style guns are incredibly accurate and you'll get a custom action, or at the least a trued remington, on a good stock platform that would fit your needs.
http://benchrest.com/shooterscorner/thelist.pdf
V28. 6BR Varmint, Mod. 700 BDL trued action; SS Shilen varmint taper bbl 27†X 10T factory nk <300 rnds; H&S Prec. Syn varmint stock
w/glassbedding over bedding block; Rem crisp 2 lb 40X trig; Inclu: Burris Pos-Align 1†mnts; Gunsmith: B. Monell; Exc cond. Great 9¾ lb rig for
reaching out w/o recoil. $1049.,$1675. invested) 3329 ser #G6238342
V37.22BR Custom Rem, w/trued Rem 700 action, converted to single shot; Shilen SS fluted 26â€X14T bbl, w/.247 nk & 400 rnds; McMillan f-glass hunter
class model stock w/alum pillar glassbedding; Factory 2 lb trig; Gunsmith: Borden Accuracy; Bore Exc. Stock need some sanding & maybe painting.
Great chance for a very accurate custom Varminter. $895.,c.1600. orig invest.)3402 ser #6230619
Consider this:
Cost of your remington.
Cost of new barrel, chamber job, and fitting of barrel to your action by a competent smith probably $500 or therabouts.
scope rings and bases - $60-100
new stock $2-500 depending on what you go for and inletting available.
You may even be able to get a deal in the classifieds here where a guy will sell the whole deal: gun, rings/bases, and dies.
Hope this helps. Whichever way you go have fun doing it.
Mike