As I remember a guy on a 26' sail boat going to Catalina, had a problem, didn't know how to start the engine, I think it was 65 days before the coast guard in coasta rico picked him up.
As for sleeping at sea, as long as you have faith in those you sail with, You get used to the movement. I genneraly have more trouble when it stops.
As for boats there are a lot of boats, But you have to make them sea worthy. Thats why new boats are commissioned.
I would seggest you start by signing on as a deck hand on a race from del rey to Mexico, Come back with the boat. The southern run is easy, the 2 knot current will get you 48 miles a day. coming back thats a different story.
I don't cross the Mexican border anymore, but once you have your passport, call the Mexican consulat and ask them what papers, you need for the boat.