You haven't given us enough detail for exact information but there are several options. Assuming that your ship, whichever one it is, will be taking passengers on board at about 2pm then I can tell you that both docks in S'ton are reasonably (within a 30 minute walk) from the Bus station and the "Central" railway station but with luggage I would get a taxi from either. Car Parking (sometimes free) is available at the Docks. Staying overnight (with the help of Yellow Pages) could take a lot of the hassle out if you can afford the time. Your best bet really is to talk, not write, a good cruise agent, like www.CRUISE.co.uk on 0800 091 1629 and talk about your situation. Neil Dow.
There are basically 3 ways to travel
1. Drive and park by car
2. Take the train to Southampton
3. Evesway travel operate a coach service for P&O and Princess and pick up from Chester. Other cruise comapnies operate similar coach links