I've done the Med cruise three times, one the first week of May and twice in October. October is nice but can be rainy, but May was almost perfect weather. I would avoid the summer months at all costs due to the heat and crowds in the ports and you also have a lot more children on the ships in the summer months.
Whatever you decide, try to fly in at least one day prior to the start of the cruise to rest and possibly see some of the origination city. Having the day or two buffer up front also allows your luggage extra time to catch up if necessary. I've been on cruises where people did not get their luggage until 5 or 6 days into the cruise. If you plan to fly in the day of the cruise, pack a couple of changes in your carry on bags.
The earlier you book your cruise, the more choices you have for planning excursions and/or private tours.
Been there - done that:
2005 Holiday, Sensation, Conquest,
2006 Conquest, Celebration, Holiday,
2007 Freedom Grand Med, Holiday
2008 Fantasy & Sensation,
2009 Fantasy, Holiday & Dream Grand Med
2010 Fantasy and B2B Elation
2011 Monarch of the Seas
2012 Booked - Breeze from Barcelona 12 days