My current .338 rifle is a wildcat based on the .280 Rem case. I have previously owned a .338 Win Mag, but I was a beginning handloader when I traded it off, so I never got a good feel for its true performance limits. My opinions and recommendations are based on my experimentation with my current rifle (and extrapolating a bit for the 338 Win Mag).
I am going to start with barrel length and twist. IME, the 338 bore is not particularly sensitive to barrel length. That is especially true for the smaller cased 338 chamberings. My 338 has a 26" barrel. Muzzle velocity at max vs an identically chambered rifle with a 24" barrel was a grand total of 26fps higher. IMO, going longer than 26" will gain you very little. The standard twist for the 338 Win Mag is 1 in 10. This has held up fairly well even for newer cup and core bullet designs. However, the availability of some very good lathe turned solids justifies going to something in the vicinity of 1 in 9. This will give you the flexibility to use the full range of the best bullets available, with no down side. My 338 wears a 1 in 9.3 Krieger and works well with a variety of bullets, light to heavy. Go with a heavy enough profile to accommodate a muzzle brake. I recommend a four or five port side discharge type brake. This will allow you to shoot in relative comfort.
Powder selection for the 338 Win Mag can be tricky if loading for max velocity with heavy bullets. Dense, high energy powders are the key for this. For a long time, the 338 Win Mag existed in a sort of No Man's Land in terms of case capacity. It didn't have enough capacity to utilize slower burning powders to push heavy bullets to useful velocities. But, it had too much case capacity to take full advantage when dense, high energy powders (such as RL-17 and H100V) became available. My .280 based 338 was able to achieve impressive velocities (relative to case size) with both 250 (2850+) and 285 (2650+) grain bullets pushed by RL26. The problem was that RL26 really needed a larger case to work properly. In my .280 case, RL26 fouled excessively and built up quickly, forcing me to discontinue its use. When RL26 is utilized in a combination of case capacity, bore diameter, and bullet weight that matches its burn rate, this problem goes away. Based on my experiences with RL26, I would expect the 338 Win Mag to offer near ideal case capacity to utilize it to its potential with 250+ grain bullets. Vihtavuori N560 will also work well. N565 may also be worth a try if you find yourself reaching max with N560 before filling the Win Mag case.
As for bullet selection, I believe the 250's will prove to offer the best overall performance from the Win Mag case. At the ranges you plan to shoot, even with proper throating and the right powders, I am not sure you will be able to push the 300's fast enough to offer enough advantage over the 250's to make it worthwhile. Something like the Hornady 285 ELD-M might work, but the amount of freebore required to make that bullet work will cost you performance with the 250's. I recommend that you start with the 250 Berger EH and/or the Cutting Edge 250 Lazer. You should be able to push either one well above 2900 from a 26" barrel, with accuracy.
For what you want to do, obtaining good brass will be critical to your success and is worth the time and trouble. Unlike the RUM or Lapua, tough, good quality brass is not readily available for the Win Mag. Norma is probably the best 338 Win Mag brass you will be able to find, but it is not especially tough. Necking up and fireforming Peterson or ADG 7mm Rem Mag brass may be your best option.
