ExXB
I have done the GVA-LHR then Southampton a few times to join cruises, my next at the end of May.
Not saying it's the best route, but I have always taken the train from LHR to Paddington then taxi to Waterloo and jumped on the train there. Train from Waterloo to Southampton is under 1.5 hours (might even be 1.25 hours)
I was checking tickets/timetables for end of May but they do not seem to be published yet, but don't forget the megatrain website, they often have £1 fares but not often on the most convenient trains.
For luggage, my bag has never been over 16KG even for a 14 nighter, but I understand women have different requirements
(I never bother with a tux either, infact I've more or less given up on formal nights altogether, just can't be bothered with them and just wear a normal dark suit - but if needed a Tux can be rented onboard (certainly on Princess))