Early days for you yet.. Do you know that you can arrange legal liveaboard moorage? or do you plan to 'anchor off' - and if so are there good, safe, secure areas to do that and is there handy shore access?
There are plenty of 30 footers that would be decent liveaboards for a single person, the Catalina 30, or Newport 30 probably would be good inexpensive candidates. However I think you need to spend some time researching boats, the associated costs and maintenance issues before committing to this plan. It all sounds romantic and all, but in reality legal liveaboard (with services like power etc) is rarely truly a 'cheap' way to live.
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)