I also like to board as soon as possible if nothing but to relax and unpack, especially since you can go to your cabin right away now. Then go to lunch. We also tend to go to the port city at least a day ahead of time so have already done the "sightseeing" thing before we board.
I'll go with "b", too. We've paid for that first day and we want to get our money's worth . We always go into the port a day or two early, so we don't need to delay boarding to see the port city. Likewise, we don't need to board and then get off to sightsee.
We like to get onboard ASAP, deposit our carry on luggage in the cabin, then explore the ship and eat lunch in the dining room.
"A truly happy person is one who can enjoy the scenery on a detour."
Golden Princess 2009 Carnival Conquest 2010
Grand Princess 2010 Island Princess 2011
Grand Princess 2011 Carnival Magic 2012
Carnival Dream 2012 Island Princess 2013
Carnival Magic 2013 Carnival Legend 2014
Carnival Magic 2015 Coral Princess 2015