As stated, just do your research. Cruise line transfers are usually competitive if it's one or two people, but for 7, you may be better off taking a cab to the port. However, with as many people as you have, you will probably need 2 cabs, so that's $50 one way ($25 per CAB, not per person). This is from the Miami Airport to the Port of Miami.
In doing research for my most recent cruise, I saw that I could save $200 by flying into Fort Lauderdale, then taking a shuttle to Miami, but didn't end up doing that cruise.
I think you are on the right track, however, to fly in the day before, especially if you have to connect flights.
As far as shore excursions, I've always booked ahead of time. If you don't want to do Carnival, then you can try shoretrips.com.
2007 - Majesty of the Seas
2009 - Enchantment of the Seas
2010 - Freedom of the Seas