The Primitivo has a special place in my heart. It is just right for me. Quiet walking but meeting up night after night with practically the same group as there are not so many options that groups get split up. It is gaining in porpularity so I would avoid arriving in albergues too late in the afternoon, especially as there will be three of you and I suppose you will prefer to bunk close to each other.
In Oviedo, don't miss the Naranco sites, up on the hill behind the train station. You can actually start your Camino from there. Other great "musts", for all sorts of reasons include The menu del dia at casa Pachon in Salas (followed by a nap as you won't be able to walk after that), a night's spluge in the albergue is the hotel Palacio de Meras in Tineo, a night in San Juan de Villapanada (a simple traditional albergue with a brilliant hospitalero), a night at David's albergue in Bodeyana, and of course the walk on the Hospitales route, but only if the weather is good.
Have a wonderful time!