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First cruise for my wife and I last April (2007). THOROUGHLY recommend Royal Caribbean 11 Night Exotic Southern Caribbean Cruise. Food / service / shows absolutely outstanding and itinery fantastic and not too many days 'at sea'. Smallest ship in the fleet but still big enough to get lost in. If possible go for Junior suite with balcony on stern (back) of the ship. Go for it. Enjoy.
Good food in the med, try Celebrity or even Crystal, food rated well on both, youmay find a seven day cruise if you look.
Try Regent Seven Seas or Oceania Cruises and you won't go wrong. Think they are both about 70,000 tons, excellent staff, service, food and everything.