Chez Jasmin is the place to stay in Palermo in my opinion.
See my Feb 2005 review.
www.medmargroup.it for ferry schedules and fares Trapani/Tunis
Segesta Lines runs buses every 15-60 minutes from Palermo's train station to the Trapani Port. Travel time 2 hours. One way fare 7.80 Euros. Very, very easy. Very comfortable, air conditioned buses with reclining seats.
You walk 100 yards from the bus stop at the Trapani Port to your ship.