Go to hodgdon.com and click your way in to their 350 RM section, and you'll find it likes pretty much any of the fast'ish (3031) to medium-fast (4895/4064/H335/BL-C2/etc..) powders. 2015BR and W748 work pretty well, too.
In my (you know the drill, start low, work up, etc..) 700 Classic, I've found the 200 Hornady Spire Point and 58 I-4895 with R-P 9-1/2M's at 2.810" OAL gives about 2,650 FPS, 1 - 1.5" 5 shot groups and instant death on whitetails. According to the manuals, you should be able to get to 2,800 with 200's, but 2650 works so well I've seen no reason to change.
The superb Sierra 225 GameKing and a couple grains less powder gives around 2,500 FPS and such good grouping that I wonder just how well it would do with a solid shooter behind the trigger.
FWIW - there's a 350 RM thread going over at AccurateReloading right now - 350 Rem Mag - Topic