A comment by trainer on Friday open gun advice thread
I have a Marlin 1894cs in .357 that is a ball to shoot, but not for hunting critters as large as you need to. I've been shooting a Marlin 336 30-30 a lot lately and it would be more to your liking...shells are ejected to the side allowing a scope for old farts...unlike the Winchester. I also have a Yugo SKS that I customized (read bubba'd), and this is the trunk rifle of choice out west right now. The SKS has never failed to feed, fire, or fling in thousands of rounds.
Much of course depends on your budget, but for game in Europe, I wouldn't think you would need much more than a 6.5x55mm Swede. They can be found in the original Swedish Mauser configuration if you are a purist, or just about any modern rifle manufacturer has a swede. Ruger makes the Swede in beautiful single shot and bolt action models.
The round is extremely accurate with low recoil, yet has the 100+ year history of military use behind it.
I don't hunt, so my guns tend to be for fun or SHTF.