I suggest you browse trough the archives of "On The Wire" from the good old "beachcats" days. You will find lots of experiences, tips and advice there.

http://www.thebeachcats.com/OnTheWire/catsail.com/index.html
(where are the rest of the issues??)

In addition, we have our own offshore solo catsailing guru here. He goes under the name "Hobiegary", and you can learn what you need to know from him (why do I feel like I just presented "The Stig" of offshore catsailing <img src="http://www.catsailor.com/forums/images/graemlins/grin.gif" alt="" /> ).

If you want to sail solo and offshore, a catamaran is infinitely better suited for this than a monohull dinghy in my opinion. Not only becouse it is faster, but it is controllable in strong winds/rough seas due to its hull configuration.
The downside to cats are the high loads and the dangers of capsizing or "going turtle". But if you know what you do (have the experience needed), you can sail a 18 footer across the atlantic ocean. It has been done several times, but dont expect it to be fun. You will probably give in before the boat does..