Carnival is a good choice for the younger crowd and many ships will have singles parties. There will be a cruise director who is in charge of on board activities you can get specific info from them. Daily activities will be in your planner which is delivered to your room each night so you can plan the next day.
I love Cozumel as a port you will find the range of choices for excursions to be dizzying. On my cruise there last week we had 6 pages of choices on that port. Swimming with dolphins, zipline, and horseback riding are always popular choices though you can also just go to the beach for the day. Personally I enjoyed snorkeling under ground in a cavern, very unique though not the best choice if your claustrophobic.
In progresso if your into history you can visit the Chichen Itza mayan ruins it's one of the seven wonders of the world. Also many beach choices there.
Its hard not to have a good time on a cruise, enjoy!