Within the US.. book your own air. Go the DAY before (the whole day and not the evening). That will make sure you get there. Doing your own air provides you with the ability to use upgrades and other things from your favorite airline.
Outside the US (specifically Start at A and End at B) is difficult. This as was mentioned is Open Jaw. I am doing QM2 NY-Southampton this summer. Cruiseline airfare was like $450 (the credit they gave me). My own ticket was $1200... but I am confirmed trans-atlantic in business class with an upgrade. My traveling companion is on a free ticket (tho a waste of miles since AA has only round-trip free tickets).
What would I suggest? I have booked on my own flights to New Zealand and back from Australia .. again with upgrades for cheaper than what the cruise line wanted. That said .. another cruise I almost missed the ship with my own airbooking .. when my flight cancelled (I did not go the day before!). There are many variables (even time of year topics)
There are several thoughts on where to stay the night before. Someone mentioned near the dock. I personally think near the airport with free shuttle to the airport would work. Fly in, take hotel free shuttle to property, stay, take free shuttle back to airport, go to luggage and find your cruise-line Rep and take the cruise transfer (you will have to pay for this but they normally take walk-up - non coupon - cruisers).
As far as the return. Call the cruise line ask when you can book a returning flight. Yea the ship arrives at 7/8am and the cruise line says not before 12:30... BELIEVE THEM! Then you can take their shuttle (purser will arrange and you pay) OR take a taxi. From FLL I took a cab and was able to standby on an earlier flight (thanks to EXP on AA) .. but it is not something to count on. LISTEN to the cruise line .. and follow. There have been many posts here freaking out that the ship arrives at 8am and they have a 10:30plane and will they make it. Answer mostly NO!
As a first time cruiser consider Caribbean or Alaska first before venturing onto something 'exotic' like Australia or Greece (for example only). You have a lot to learn from your first cruise .. the transfers are just one part! There is the seating (second), table size (large), the cabin (balcony minimum) and the ship line (loads of choices) and then the shore excursions/mix of sea/shore days (more sea). (these comments are my own)!
I personally love sea days. On port days I sleep in and will take a late morning or afternoon tour (never the 8am tour). Its nice to have an almost empty ship to yourself.
Also, length. Took a 4 day cruise.. hated it (waiter did not know my preferences or anything) . have had several 7 day cruises .. loved .. and also a 14 day panama canal cruise ... LOVED it but hard to get off from work... also a 14 day Australia cruise .... REALLY LOVED it but takes 2-3 days to get there and a long day getting home so almost three weeks shot from work.
Ask this forum your questions.. they may snicker at first and then give you a good answer. (I still cannot be bothered with Port and Starboard .. yes Fore and Aft makes sense)
Once you narrow down cruise #1 option, as questions with details.