Welcome to Sailnet. I'd highly recommend you read this post
to get the most out of your time here on sailnet.
If you're looking to liveaboard a trimaran, I would highly recommend you not get a folding design. The folding designs will often have less space aboard due to their being designed to accommodate the folding requirement.
However, a fixed beam trimaran is often very difficult to find a slip for and often much more expensive to haul and launch. There are some very good designs that would work for living aboard and long distance cruising.
Be aware, that a 30-40' trimaran is a fairly expensive boat to purchase, own and maintain. I'd ask what your rough budget is for purchasing the boat, and highly recommend you set aside at least 15% of your total budget for refitting, modifying and upgrading whatever boat you do get, since sailboats are not like cars, where they are ready to go just off the lot. Most will require some modification to make them work for the way you will sail it.
Another option would be to make the boat yourself. If you have the resources and skills, you can make a 35' trimaran in about two years.
I'd also recommend reading the following books:
Sensible Cruising, by Don Casey, Lew Hackler
The Cruising Multihull, by Chris White
Multihull Voyaging, by Thomas Firth Jones
It would help if you said how old you are, and what resources you have... the more information you give about yourself, the better advice you can generally get.