We use 316 tig rods for welding 308 stainless i think it was, fine no problems. if i remember correctly 316 is high grade stainless, im going to say marine grade (and possibly get shouted at for being wrong), 304 and 308 are lower grades of stainless (going to get shouted at again for that). Using a better grade of filler wire on a lower grade of stainless is fine, but i wouldnt recommend using 304,308 grade filler wire on 316 stainless if that makes sense
The 316 will weld it, 308l is probably the more favoured though.
Gas wise, what gas have you got, Inomaxx,stainshield etc are the ones to have, argon with a touch of oxygen iirc.