Hi Martin! I recommend the Explorer of the Seas. I just got back today and there were passengers from everywhere. Lot of europeans, people from all over US and aussies like you... You'll love the ship... It has great entertainment. Most of college/university students go on vacation during Spring Break (around Easter time, late April and already past) and Summer Time which is anytime from now until the end of August. Doesn't matter who you come with you'll have a blast!!! Asides from the great experience the cruiseship has to offer, you'll have Miami and wonderful South Beach!!! Come check it out! I've heard good things about the Paradise, but is my understanding that is more oriented to an older crowd... The ship is smaller too... As far as smoking sections, I've travelled in Royal Caribbean twice and you can only smoke out in the decks.
P.S. - Hopefully I was helpful :-)