Serre Chevalier is one linked ski area and several places to sleep. The resort’s own description runs from Monêtier-les-Bains to La Salle-les-Alpes and Saint-Chaffrey, with a piste back into Briançon. Briançon is a town, which helps if someone in the party is not skiing. The higher villages are quieter at night and closer to the snow.
Montgenèvre is a separate resort on the pass, at about 1,860 m, with its own French pistes and a link toward the Italian side of the Via Lattea. Stay there if the freeride and ski-mountaineering events are the reason for the trip. Stay in Briançon if you want one base for both resorts and you have a car or a bus plan. They are not ski-in to each other.
Turin is the airport that matches this valley. Geneva is a long transfer. Factor that before you compare a room rate.