Where are you coming from? You asked for London airports but there is also an airport in Southampton - with flights from Paris (Orly) and Amsterdam (as you mentioned Eurostar) - and from there you can either take a train and taxi or a direct bus (the U1) from the airport to the port.

The train from London isn't quite as expensive as you say - it's £52 single for a ticket valid on any train all day from London Waterloo, or £41 single for a ticket valid on any train leaving London after 12:01. However, if you arrive at Heathrow, there's a direct National Express coach to Southampton with tickets "from £18.70".

From Gatwick there are direct trains to Southampton - without travelling via London - for which a single ticket is £20, available on the day.

The other London airports (Luton, Stansted, City and Southend) are on the other side of London and you'd need to cross London for all of them - which as you have a heavy suitcase is probably less than optimal. If you have no choice but to fly into one of them, Luton would allow you to take Thameslink through London and change at London Bridge onto a direct Southampton train which, although it's slower than the Waterloo services, would reduce the number of changes you have to make with your suitcase.

For completeness, there are direct rail services from Birmingham International to Southampton as well, if Birmingham is better for your timings - however in almost all cases you'd be able to fly to either Gatwick or Southampton instead and those would be better gateways.

If you can commit to a specific train, you can probably also book an advance ticket which is only valid on one service (if you miss it the ticket isn't valid) but for which tickets are available from £3. It may make sense to book a couple of these for different trains as it will still work out cheaper than a flexible on-the-day ticket.

Where are you coming from? You asked for London airports but there is also an airport in Southampton - with flights from Paris (Orly) and Amsterdam (as you mentioned Eurostar) - and from there you can either take a train and taxi or a direct bus (the U1) from the airport to the port.

The train from London isn't quite as expensive as you say - it's £52 single for a ticket valid on any train all day from London Waterloo, or £41 single for a ticket valid on any train leaving London after 12:01. However, if you arrive at Heathrow, there's a direct National Express coach to Southampton with tickets "from £18.70".

From Gatwick there are direct trains to Southampton - without travelling via London - for which a single ticket is £20, available on the day.

The other London airports (Luton, Stansted, City and Southend) are on the other side of London and you'd need to cross London for all of them - which as you have a heavy suitcase is probably less than optimal. If you have no choice but to fly into one of them, Luton would allow you to take Thameslink through London and change at East Croydon (or stations between there and Three Bridges) onto a direct Southampton train which, although slower than the Waterloo services, would reduce the number of changes you have to make with your suitcase.

For completeness, there are direct rail services from Birmingham International to Southampton as well, if Birmingham is better for your timings - however in almost all cases you'd be able to fly to either Gatwick or Southampton instead and those would be better gateways.

If you can commit to a specific train, you can probably also book an advance ticket which is only valid on one service (if you miss it the ticket isn't valid) but for which tickets are available from £3. It may make sense to book a couple of these for different trains as it will still work out cheaper than a flexible on-the-day ticket.