I don't know what sort of "sniper school" you are training in. Is this is military, civilian or what kind of sniper training?
I thought for military schools they have their own custom modified versions of some civilian rifles. In know the Marines snipers do and they have special teams who do all hand loading for them.
My understanding that aside from some of those teams going to the very long range AS50 and Barrett L82A1 (military designation XM107) .50-caliber semi-auto sniper rifles that a very significant number of them shoot .300 WM for it's longer range, flat trajectory with less affect by wind than some lighter calibers.
If you have a choice, check out bolt actions by Tikka, Sako, Remington 700 BDL, too. The former can properly shot can consistently put grouping in sub-minute of angle. Sako makes models specifically for use by snipers, but the others are very adaptable it sounds like.
Tikka/Sako also have very smooth adjustable triggers, stiff floating barrels and strong actions. The built in rail on top of the receiver keeps the mounts rock solid.
http://world.guns.ru/sniper/sn22-e.htm
T3 Tactical - http://www.berettausa.com/product/rifles/series_page.cfm?currentseries=27
Otherwise, ask experienced persons who've taken the same training you're in what they recommend.