Presently shooting a 240gr/300Rum, and working on my version of the 338-300RUM. I call it the 338 Mystic and is a maxed out improved RUM case. Similar to the 338 Tomahawk.
With these long bullets, you can forget about feeding from the mag unless you want to loose a lot of powder space. I have set mine up as single shots.
The biggest benefit over the Lapua is bolt face options. All manf will make a 'belted magnum' bolt face so will work with the RUM family. Very few make one big enough for the Rigby/Lapua/Wby case so options are greatly reduced.
I have built all my LR cannons on Enfield P14/17 actions and these worked superbly. Very strong and inexpensive to boot.
Go as long a barrel as you can handle. 35 to 36" does make a difference for these big case monsters.
Also, think heavy and/or muzzle brake
. I don't enjoy recoil and these do give a very solid push. My 300RUM weighs 35lbs w/brake. My 338 Mystic will probably weigh around 45lbs w/brake. I can spot my own shots.
If the 338 Lapua ever becomes a NATO cartridge, then the story will change. There will be lots more options and brass will be cheap. For right now, the RUM is the best big case magnum when you balance performance and cost.
Don't forget the 7mm too. With 162/168 and the new 175gr MK, they can deliver a pretty powerful punch at 1000yds. Certainly alot cheaper to shoot. Would look at the 7WSM, Dakota, STW or RUM depending on how long a barrel and weight I wanted.