Your question is almost too broad... there are books on the subject.
Need to qualify as to your experience, and projected needs. In a way offshore and liveaboard are somewhat mutually exclusive at least if you are looking for lots of space in a liveaboard. There is no perfect boat.
But having said that understand that in buying a used boat - or any boat for that matter - the initial purchase price is not all that you are going to spend. Not by a long shot. I just got back from a week of outfitting my boat and the "little things" added up to 3000+ (outboard - new batteries - all the tupperware in Walmart etc)
I found yachtworld com is a very good search engine go to advanced search.
In many ways smaller is better unless your family unit contains a numper of strong athletic folks to work the
rig and sail it.
Finally there are a lot of boats out there. Do your homework, take trips, do not fall in love with anything until the surveyor says it is good or fixable in your budget. Do not be afraid to walk if a boat needs too much work.
Have fun
Todd V
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