Note, however, that only those that need to rest will be charged (although everyone ages). Also, never rest to get your hits back. Always use your Priests to heal your party at the end of a trip.
Money is really tight at the beginning of the game, but after you start going to level 3 or 4, you will be rolling in it. Think of your first party as the starter party. Don't worry too much about aging them, since you will replace them with more premium characters (Samurai, Rangers & Paladins) later. Once your starter party can reach the mid levels and can generate a good supply of gold, start working on your premium characters and then only rest in the best inn (but NEVER rest to regain hits).