One rope is all you need.
Some people will use 7.7 or 8.2mm - I don't have a problem taking a low-factor fall on such ropes, but getting a prusik or acender to bite can be difficult.
I have chosen a 9.2mm 35m rope, which will also work for harder climbing when required, at the cost of about 0.5kg. For two people 20-30m would be fine.
A dry rope is a very good idea for glaciers.
Whatever you choose, practice "falling" with a pack on, and climbing the rope with prusiks. I prefer Tiblocs, some don't. Try it yourself and make sure you have a system that works.