It costs 100 times the Rank above your current Rank to achieve the next Rank. If you have enough Prestige to achieve the next Rank, you must spend it to do so. Thus a Rank 1 character would have to spend 200 Prestige to go to Rank 2. You may save leftover Prestige.
Skill increase is paid for with Experience in the same way. A character with a 0 Piloting skill may spend 100 Experience to make it level 1. If they still have 200 Experience left, they may spend it to raise their Piloting again to level 2. You may save leftover Experience.