Hi Erik from a very Sunny Southampton,
You are quite right that the easiest way is by train, they run up to 3 times an hour, but if you are coming down at the weekend, please be aware that there are major rail works just before you get to Southampton & have to change to a bus service (provided at no extrac cost from the last station). When buying your ticket, make sure you get one to Southampton Central, apart from a few stations in the outskirts, there is also one called Southhampton Parkway, which is for the local airport. Once you get to the station, it is an easy taxi ride, or couple of mile walk hauling your luggage.
Make sure you know which terminal you are using, there are currently 3 in Southampton with a 4th (for P&O) being opened in May.
As for costs, you can normally get a few pounds off if you buy before arriving in the country, but may have to commit to a set time. It usually isn't a great saving, so by all means check, but don't expect a bargain (http://www.thetrainline.com
A good budget way of travelling down is to take the National Express Coach from London Victoria, via Heathrow Airport down to Southampton (www.nationalexpress.com
), this is well worth checking in advance as they often have £1.00 tickets. The Southampton terminal is just below the main railway station as you look at a map.
Finally, assuming that you have left your private helicopter at home ;o) you can taxi to the port, it will cost around £100 each waym, but worth negostiating with a few comapnies if this is of interest. I think that there is a taxi company owner from the London area who comes onto this site, so he may be able to give you a price.
As for getting back to Heathrow, you again have the choice of the National Express coach which is direct into Heathrow, the trains will require at least one change, or traveling into London, then getting across town & back out to
the Airport - no easy feat with luggage.
NCL will almost certainly do a transfer, so it would be worth costing that option before making your decision.
Hope at least some of this has helped, if you want any more info, please feel free to ask.
Have a great time,
Alan & Katrina