Since all my information comes from third parties, i'd go with a m24 myself, when a gun is endorsed by the US militairy for about.. 40 years? It can't be complete shit. :)
On the side i would get maself a M14 with a bipod, though i'm not sure if that would work for "sniping" as much as it would for "marksman-ing", if there is a difference... *trails off*
M14 are highly accurate semi autos for sniping. Useful to out in the 1000 meter range where the .308 starts becoming less likely to do much. Only issue is cost and maintaince. Takes alot of time to keep an M14/M1A in that state of precision. More than your average shooter can afford.
M24 is just a souped up Remington 700. The Marines M40 is just a souped up Winchester model 70. All good sniper rifles were at one time a hunting rifle for the most part. That purpose built stuff really (Accuracy International AW series, PSG1/MSG90, Sako TRG) offers no advantages other than additional price concerns.
The M40 is a Remington 700 as well. They designed it and the Army decided they'd copycat. Both are beautiful. If you're just getting into it and are on a bit of a budget, I'd have to go with the crowd and say something along the lines of the Remington 700. It's a nice bolt-action rifle that certainly makes enough noise, but fires well. It's not horrible as far as maintenance is concerned and you can get one for under $300. I'd also suggest and older Russian rifle, but you won't get near the range out of it.
You can get a used Remington 700 for $400. That's a high-performance rifle not unlike the M40A1 the Marines [US] use for sniping. If you get that you'll never need another "sniping" rifle ever again.
EDIT: I only responded to the initial post.