Sniping in the first room
When you arrive on the alien ship courtesy of the grav-lift, one strategy is to do a lot of rushing around from door to door, trying to blitz the enemy at close range as they arrive (prior to the Hunters). I'd rate this the most effective plan for containing the enemy and thereby keeping Marine casualties to a minimum. But you can also be quite effective using the sniper rifle as follows.
There's a place on the edge of the central circle where you have a clear view of all four doors the enemy use. Stand there. Keeping an eye on your motion tracker, use the sniper rifle to take down most of the enemy the moment they appear, and especially the Elites. Of course, you can also lob grenades so they explode just as the doors open. You may need to dodge around occasionally or quickly root out any enemies that manage to get behind cover, but always try to get back to your base point and keep in control.