if I had no other choice I believe that I could narrow it down to 6 options. I have a little over a dozen now but many of them are older guns that I bought just for the sake of collecting. if I had to limit them however for the sake of discussion(also I am making a wild guess as to the type of game I could possibly be hunting in sweden)
a bolt action .243 would be able to handle any deer or wolf sized game given 100gr bullets or more and is a good multipurpose round for both woods and mountains so I think that one of those would be a good option. 257 roberts would also do just fine but I would guess that it would be hard to come by in Sweden.
since you are in sweden I would wager a guess that 6.5 swede, 8 Mauser, 30-06 Springfield and 303 British are all commonly available ammo so I would say that larger game such as bears would be within the realm of all of those rounds.
I don't know if you are limited by action type but a nice semi automatic 22lr chambered rifle like a Ruger 10/22 or Marlin 60 would be just the ticket for rabbits and other small game.
lastly is bird hunting, a decent shotgun, either over and under or pump action in 12 gauge would serve you fine for bird hunting.
that is about all I could think of for necessities but a nice gun to augment a collection like that would be a combination shotgun/centerfire rifle. that just makes it simple when you only have to pack one gun when you expect to find both large game and foul.
that is just the way I see it. many Americans take unlimited gun options for granted and have 2 in every caliber but if we were limited by how many we were allowed to own then we would all have to be a bit more picky about the guns we buy and every one would have it's own purpose.
all guns lost in a tragic smelting accident.
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