The M-700 in .350 magnum was my introduction to powerful rifles in the early '70s. It wasn't long before the stock crackedforward through the forend checkering and back halfway through the pistol grip. So if your M-700 has the old thin stock with press checkering, look for cracks. If its not cracked chances are its in nearly unfired condition so unless you want to upgrade the stock, get it glass and pillar bedded.
The .350 magnum cartridge is not as good a choice as is the .35 Whelen, IMHO. While capacity is the same, the short .350 doesn't handle long bullets as well as the longer cartridge does, and the throat is shorter. When I had my .350, it was all but impossible to load to the cartridge's potential with the 270 gr Speer, and today a similar problem would occur with the heavier "long for weight" TSXs and similar mono-metal bullets, to say nothing of a heavy weight Woodleigh. The cartridge would do better in a long action rifle, with a long throated chamber, so the bullet could be seated out to optimize the powder capacity. But once chambered in a long action rifle, the .350 has little advantage over the .35 Whelen, and none at all over the .358 Norma. The .350 magnum rifle I'd watch out for today is undoubtedly the M-7 custom shop model with the kevlar stock. I've handled 2 in the last 2 weeks, and they are sweethearts.
Its been a long time since I've loaded for a .350, but if I was at it today I'd look for the heaviest round nose, lead core, bullet that would keep me within the allowable 2.8" COAL, and I'd back it with ball powder, perhaps H335 or W-748.