You will probably get different responses here too!
I suggest a minimum length of 30m for 3 people but only if there are other folk around to assist with any serious crevasse mishaps. I use a 50m 8mm half rope for such things to save weight. It is dry treated, although I'm not sure if that really helps.
Obviously a full weight rope would be a better buy if you wanted to use it for more serious things later.
50m for glacier travel. The ends are coiled into a "chest harness" leaving the appropriate distance between them. This coiled rope is then used to for the rescue if someone falls in (and to prevent inversion for the person falling in). If you're not sure what this means look it up and get training. Dry treatment is worth it for glacier travel. Wet and frozen ropes are heavy and hard to handle.