If you are going to add a suppressor to a 308, I don't think I'd consider anything other than a 16". If not I'd go at least 18 or 20. I don't like the blast of a 16" 308, especially if it has a muzzle brake.
Profile? Sorry, I like em heavy and I like to shoot them prone. Maybe someone else will chime in.
ETA: Faxon makes some different 308 barrels -
http://faxonfirearms.com/barrels/?sort=pricedesc