Don't take the above advice re Southampton! You and your partner will want to experience new countries and new cultures ASAP so get on a plane and pick up your ship abroad. Sailing from Southampton means that you'll have at least 1 day at sea and it can be rough crossing the Bay of Biscay if you are heading south. For a first time cruiser try Ocean Village or Island Cruises. They bundle up the flight and cruise in an attractively priced package.
Broadly speaking yes if you book through a decent agent they will tell you what your paying for,you can book your own flights and probably save a few quid but if the cruise company take care of it all if there are travel problems you are not on your own.Personally i would book a cruise going from Southampton no 3 hour waits or baggage allowances to worry about and see if anyone is offering free parking or coach travel,good luck .