In Halo 1 It really depended on what I was up against. Pretty much anything and the assault rifle was cool with me unless I was low on ammo. My favorite combo for taking down the Elites is to use the Assault Rifle with the Plasma Rifle. I use that to drop their shields with plasma and drop them with the Assault.
In Halo 2 it is more a matter of duel wielding for me. Preferably 2 Sub Machine guns with a Battle Rifle for back up. Though with the reworked shield system the shotgun and battle rifle combo is nice for alternating between flood and convenant.