If you can afford a Zeiss Diavari I bet you could afford a Sako.

Tikka is made by Sako. They are very similar rifles but the Tikka is built to a lower price point with a few plastic parts, etc. They are both very good and VERY accurate rifles. I currently have a Tikka in 338 Win Mag and have a Sako on the way in the same caliber.

If I were in your position I would get a used Sako AV(A five) in 300 Winchester Magnum. Great round with lots of range. Doesn't kick bad and will kill everything you listed very cleanly. You can get a used Sako AV for around 800 bucks in the states so only a couple hundred more then a Tikka.

If you dont want the 300 Win Mag and feel better with a 308 then get the 308 as both rifles are chambered in both calibers.

Whether you go with Sako or Tikka they will both be Tack Drivers.

If you are interested I am selling a Leupold Mark 4 8.5-25X50mm. It is an excellent Long Range scope. The money you would save over the Zeiss could get you from the Tikka to a Sako without sacrificing scope quality or range. The scope is basically brand new and retails anywhere from 1300 USD. I would sell it for less then 1000. Website below;

http://www.leupold.com/products/tactical_products/Mark_4_8_5-25x50mm_LRT_M1.htm