I agree with Ida you need an agent, they have specialist knowledge and will match you with a fantastic cruiseline I'm sure.
Some in laws of ours are Florida buffs and wanted something different. They have just enjoyed their first cruise with Royal Caribbean. They are converted and can't wait to go again. However they said the cost was very different as USA looks cheaper (£££-$$$) compaired to crusing (don't forget your food is included on cruise) having said that you could look on the internet once you have decided who with and where to go, you may get a bargain youself.
May I suggest that you talk to a cruise agent because you seem to want several different things which need us to ask more questions before we can answer whereas they will answer you immediately or fairly quickly. The sort of questions I have in mind are: What do you mean by "no dressing up", what criteria do you have when you say a balcony with deck information, what do you expect to pay, that is are you looking for a bargain low price cruise or splash out on something more expensive than average or something in the middle, how essential to your plans is Southampton and what do you expect to find on a cruise. Just a few of the questions that would point anyone in the right direction. You have plenty of time especially as that time of year is when the children have stopped holidaying (in the main) and the catering and hotel industry are still working and not able to take their yearly break. So good luck .... Neil.