Re: 338 Ultra Mag
Recoil first - it's exactly double that of a 7mm Rem Mag. You can either create a heavy gun that tames the recoil, or put a brake on it, or do both!
As for the barrel length, Remington puts a 26" barrel on their RUMs, and I suspect that something more like a 27" or 28" barrel is in order (minimum length). I've heard of some people putting even longer barrels on them with good results. The heavier the bullet you plan on shooting the more improvement you'll get with a longer barrel.
Sounds like you're building a hunting rifle. Anything longer than 26" will do pretty good.
Mark in Utah