I'm a Remington fan myself, and there's lots of stuff out there for 'em. I like a stainless rifle, and a good stock. For a hunting rifle, I prefer a fairly lightweight rifle with a shorter barrel. I like them to be 7.5-pounds or lighter, all up. With that in mind, here's what I recommend....

Remington 700 action
Light contour stainless barrel of your choosing, 22-23" inches.
McMillan Classic or Mountain Rifle stock, in the ADL configuration
Williams triggerguard
Talley lightweight 1-pc scope mounts
Leupold scope of your choosing - I like their 2.5-8x and 3.5-10x variables
Tune the factory trigger



Since you've settled on a common factory chambering, there's a lot to be said about Wilds recommendation of starting with a Remington SPS. Chop the barrel a couple of inches, recrown, tune the trigger, drop it in a McMillan, and mount up some glass in Talley LW's.

You could keep it the BDL configuration or make the change to an ADL-style, when you restock. In this particular case, you'd be staying with the factory barrel contour, so you could probably find a McMillan stock as one of their "specials" on their website. This save you a couple of bucks, but more importantly, it will eliminate the 6-month wait versus simply ordering one.