Don't bother with trying to combat the snipers. Just try to stay out of their line of fire. Your bread and butter is going to be flanking and firing off a few shots to clear out one or two guys from a space.
You can try to sprint around to wherever the snipers are and blast them, that's probably the best way to do it. Remember that some maps are just awful for shotguns. Turbine comes to mind.
You don't want to be glowing on the radar while using a gun that can't shoot past close range. Lightweight makes you ridiculous with the Remington. Chuck EMPs and C4 like candy. I prefer engineer, but others like dex or excon.