I would look into a Winchester Classic Model 70 in 338 Win Mag or 375 H&H. The 338 for Alaska. The 375 if he will wind up hunting in Africa. So, in your price range, probably the 338. Let him pick his own 375.
It's harder to find an affordable control-fed bolt action, but they offer more reliable feeds for dangerous game. Not an area to save money. I consider the larger bovines dangerous when at close quarters or wounded, like moose, American buffalo, or Cape buffalo.
Some ideas...
Outdoor Life 50 Top Guns in Last 10 Years -- my picks
http://www.outdoorlife.com/photos/gallery/guns/2011/05/best-hunting-rifles-decade
Browning T-Bolt 22LR $600
Weatherby Mark XXII 17HMR $950
T/C Venture Predator 22-250 $550, or Precision Hunter 22-250 $1,300
Ruger No. 1 Varminter 220Swift $1,400 (current cartridge)
Kimber Model 84M Classic 243Win or 308 Win $900
Tikka Whitetail Hunter 308Win $620
Browning X-Bolt 30-06 $850
Kimber 8400 Classic 30-06 $1,100
Sako 85 Finnlight 308Win $1,600 -- mountain rifle
Some reading if you like...
Hunting Guns: From Your First Rifle to a World Class Battery
http://www.chuckhawks.com/hunting_guns.htm
Heavy bovine game: .308 to .50BMG
http://www.ballisticstudies.com/Knowledgebase/Heavy+Game+Cartridge+Overview.html
Bolt Action Rifles for Dangerous Game, The Rifle Stocks
http://www.chuckhawks.com/bolt_rifles_dangerous_game.htm
http://www.chuckhawks.com/grizzly_cartridges.htm
Recommended Riflescopes
http://www.chuckhawks.com/recommended_riflescopes.htm
http://www.chuckhawks.com/scopes_price_class.htm
http://www.chuckhawks.com/compared_dangerous_game_riflescopes.htm
Prime Questions: list your priorities, rank them to your mission
1. How far is your target--max effective range
2. How tough is your target--remaining energy & bullet construction/type
3. How easy to feed the rifle, ammo & component availability
4. How easy to carry & move the rifle, weight, mobility
5. How easy is to make the shot, recoil, trajectory, wind deflection
Not important: lightest bullet with highest muzzle velocity
http://www.youtube.com/watch?v=pwG-D0HjCBQ
BrassFetcher: bullet performance in ballistic gelatin
www.brassfetcher.com/
Hope these help. ...such a thoughtful wife. ;)