A bolt or single shot...your choice.

Under 6.5 pounds naked!

A minimum 3,000fps at the muzzle with a minimum 115 grain bullet and preferably something in the 125-140 grain range.

Lots of good calibre choices. If you are going with a bolt action...you are likely looking at a short magnum. A single shot will give the choice of some of the long action calibres too. If I were building a sheep rifle today, it would be a single shot 7mm STW or a 270WSM or 300WSM in a bolt.