You need to realize that the 338-378 and 30-378 are pretty long chamberings, especially if your going to use a long range match type bullet for long range shooting and hunting. Or the tipped big game bullets such as the Nolser Accubond. If your building a single shot, this is much less of a concern but if your looking for a repeater, you will need a receiver that will allow you to convert it to a longer then standard magazine length.
The best receiver I have used lately for this type of rifle is the BAT model HRPIC receiver. This one has an integral recoil lug and 20 moa rail base. It is designed specifically for this class of chamberings.
It also allows you to modify it for use with the longer magazine boxes be it the Wyatt 3.900" center feed internal mag box or the new Seekins 3.990" DM system. IT can be modified to work with either of these.
Its not much heavier then a standard Rem 700 but much stronger in the critical areas allowing it to easily work with the Big Wby and Lapua class chamberings. It also works well with the medium weight barrels but I would not go much over a 1.200" straight cylinder barrel with this receiver without some bedding support on the barrel. For anything lighter, you can easily freefloat the barrel with no problem of receiver flex.
The rest really comes down to what type of rifle you want as far as stock, barrel, barrel specs and such.