A lot of marinas have a minimum LOA, usually around 30-35' for liveaboards. There is no LEGAL minimum LOA requirement for liveaboard boats AFAIK
. As to what boat to get—a lot depends on what your personal requirements are. I know of people living aboard boats as small as a Flicka (20') and a NorSea 27.
It takes a certain type of personality to liveaboard a small boat. You need to be organized and neat and prefer simplicity over luxury or material goods.
For a single person, boats as small as the Flicka are workable, only if you can deal with the lack of space, lack of amenities, etc. I'd point out that a shower is generally not available on boats less than 30' LOA, and also not a necessity for living aboard, since most marinas will have shower and restroom facilities.
More important are having a good berth—since sleeping is a major part of living aboard, and a good, workable galley, since eating is also a major part of living aboard.
As for finding a "legal" liveaboard slip, many marinas will "allow" you to liveaboard, especially if you are courteous, clean and keep your boat in tidy shape. The major opposition to living aboard at many marinas is a desire to prevent the marina from becoming host to a bunch of derelict, unkempt boats. Having some liveaboards at a marina is often a good security measure, since they are present to keep an eye on what is going on there.