Firstly, let me reassure British cruisers that Independence of the Seas is not "Butlins on Sea" as I have heard it accused of being. We chose Indy from Southampton because (a) no transatlantic flights and (b) for the two week itinerary, because we had found that on Freedom of the Seas, a week simply wasn't enough.
Embarkation: Having never cruised from a home port before, it was a real novelty to not be restricted by airline baggage allowances (if it could fit in the car, it was packed), and to be able to have a leisurely drive down to Southampton the day before the cruise. We stayed in the West Quay Premier Inn, highly recommended because of its proximity to Hollister in the neighbouring shopping centre (we have a daughter - need I say more). We shopped until we dropped, checked into the hotel where we had a peaceful night's sleep, and after a very busy breakfast on Saturday morning (4 cruise ships in port!), we checked out and were at the terminal within 5 minutes.
Here we were directed to drive to the luggage drop off point, where helpful luggage handlers took the luggage directly from the car boot, and then drove to the car park. We carried our hand luggage into the terminal and then checked in. We were reasonably early so the whole process only took 45 minutes, and we were on board before lunch!