If you are serious about reaching out to 1k, you may wish to re-think things a little. Either get an after market action, or go with something other than a remington.
-- Aftermarket action: The big plus is, any good after market action is already fully Trued and ready to be built. For instance, Lawton Machine Welcome to Lawton Precision Rifles
sells some pretty darn good actions for a reasonable price. Add in a good after market barrel such as Krieger, Bartlein, or the Lawton barrel. Lots of really great barrel makers out there. When you are done, you have "Bought once, Cried Once" and you will be happy to know that if you miss...it was *YOU*, not the stick.
-- OEM Weapon: I would actually go with a Howa, believe it or not. They do have pretty reasonable after market support. McMillan, and Manners both make stocks. At least one after market bottom metal maker makes a mag system for it, I think Badger but may be mistaken. Getting really good mounts are easy. In short, the initial quality of MFG and Design are both better than the current decade Remingtons :( Now all you reminton zealots, please feel free to Flame ON, I have my nomex undies on!
Seriously, for 1k work, Buy Once, Cry Once. Not saying you have to go Top Dollar all the way, but some things like Action, and Barrel, are simply too important to skimp very much on. Not to say you can't make a factory stick shoot well, I have seen many shoot between 1/2 to 1 moa with good loads. Then again I have seen a whole bunch that would just barely make 1 moa on a REALLY good day with the best loads you can make!
Come to think of it, I think the TC warlord comes with a 1/2 moa guarantee, and I am pretty sure there are a couple of the FN / Winchesters that have an accuracy guarantee. Both very fine rilfes. I think it was the FN Patrol that had the guarantee, but you would need to look it up.
As for Cartridge: either a 7mm of some kind, or a 30 cal of some kind. The TC Warlord comes in 300 win mag for instance. Of course the 300 WSM's are pretty nice too. The 7mm-300WSM is quite nice, and like others have said the 7Saum is pretty nice as well. The thing about the Saum line is: How long will they be around? They never really Took Off. The WSM line I believe has Norma Factory brass which is pretty nice brass. The 300 Win Mag or the 7mm Remington Mag both have truly impressive amounts of time proven components and such. Either of these last 2, you can grab some H1000, some Win LR primers, Win Cases, and one of the VLD type bullets and you are very much GTG to 1k.
Have a good one