Re: Remington Milspec 5R or wait to build custom
The 5R's trigger isn't bad at all so long as you have it adjusted correctly, a half decent gunsmith should be able to get it very nice. Mine is fine for the range, for the heat and for when its freezing and wet. You don't want to have it like a set trigger or make it a feather super light bench rest queen thing (near or a tad under 2lbs is nice enough, just be safe).
A 20 degree MOA rail will usually take most good scopes out to 1000m which is a long way for the average 308. In truth a 308 is happy to 600m and then things get a little tricky.
Scope! We all have our favorites, and the argument rages on and on and on (I like 2nd focal plane; my mounts and scope cost twice what the rifle did!). If you can use a rangefinder then mildots aren't much use. A nice fine duplex is hard to beat. Target turrets are a must for elevation and wind once you start to stretch out over 300m. Leupold, Zeiss Conquests, Bushnel plus a whole lot of others are competing for your cash. A variable ?-25x is a much as you will ever need magnification wise. A 50 objective one inch or 30mm tubes both will work just fine. Side parallax is nice. Leupold rings are good enough and do mount the scope as low as you can. Nothing wrong with second hand stuff if its from a good make.
An inexpensive cheek rest is worth it with the 5R, though a bit of foam and tape will do. The factory stock with the above mod is as good as anything (I see all to many shooters add aftermarket stocks that make their rifles too heavy to do anything other than prone). Remember there are other positions to master. The 5r is a nicely weighted rifle as is; so everything you add is weigh. You add it, you carry it. Just be careful you don't add too much.
I like the Atlas bipod if you have the cash (great investment) and with the quick release you can take it off for other positions shooting.
Finally, you really don't have to have the "best you can get" to shoot. Whatever, you can put together can work; just get out there and shoot. Most of the time it will be you not the kit. Make notes as you go along as they will beat any ballistic calculator.