Your most efficient speed on a 36'er is going to be below 8 knots. On a 30'er closer to 6.5 knots. I normally cruise at 7.5 knots or so in my 36' trawler with twin diesels. I know it doesn't sound like much difference, but if you're planning to go over 3000 miles then you want to figure it correctly.
A lot of people consider 36-40' to be the minimum for a liveaboard. I've done weeks on a 28' express cruiser with 5 people aboard, and some people do the loop in small open boats. How much space you really need is a very individual thing. I'm big on interior space. Some people prefer a large cockpit.
In the 32' range, the older Bayliners are nice loopers. Down to 30' look at the Prairie 29 or Atlantic 30, which are also older makes. Below that there are trailerable, outboard "pocket trawlers" like the Rosborough which are pretty efficient and make decent use of the limited space. These are just starting points, lots of other makes and models to choose from.