The price off brass for the 340 weatherby, 338x378 Weatherby, 338 Lapua, 338 Canadian and 330 Dakota seem to run about $40.00 a box. The brass for the 338 Rem Ultra runs about $14.00 a box slightly more than the 338 Win Mag which is about$10.00 a box.If you handload the cost of feeding a 338 isn't all that bad. I think the 338 mags are some of the more useful cartridges as they offer the trajectories and velocities of the 7MM mags and 300 mags with a lot more when they get there.
If I were just getting framiliar with the 338 I would start with the 338 Win Mag in a 700 Remington. The reasons I would start with the 338 Win is barrel life and recoil. I'm not a Remington freak but the 700 offers the length, the full length ejection port and the bottom metal to go to a 375 H&H length cartridge should you feel you need more recoil at a later time. Keep in mind it's real easy to turn a 338 Win mag into a 338 Rem Ultra mag but Its real hard to turn that 338 Ultra back into a 338 Win mag.
Have a nice evening, Rabon...