Depending on the nationality of the character, it could be quite a lot of things. However, a Finnish character would have, depending on his outfit and whether he was actually fully classified as a sniper or a support sniper either sniper rifle m/2000 (Sako TRG-42 in .338 Lapua Magnum), the heavy sniper rifle m/2000 (Barrett .50 cal in either the M82A1 or M107) or, if assigned to further down in the reserves, the sniper rifle m/85 (practically a 7.62x53mmR Mosin-Nagant action mounted on a plywood stock with a heavy free-floating bull-barrel).Of those three I've actually fired the last one (and trained other reservists in its operation) and love the old lady sincerily.
For other nationalities, I'd probably go for a bolt-action rifle like AWM or M24/M40 series. SVD could come to question as well (I have also trained with it as a reservist, though I consider it to be more of a support snipers weapon rather than a full-fledged sniper rifle). The funny thing about SVD is that is was built for use with a heavy protective vest, which makes the stock about 5cm/2" too short - a painful thing to shoot unless you have already learned about that. And the rubber 'suction cup' at the end of the original scope is also a funny one - it feels as if your eye would be just about to be sucked out of its socket when you fire the rifle.
