It's much easier to get to Twickenham from SOU than SEN: there's a railway station on the the airport with a frequent service, with just one change at Clapham Junction, (there's no need to faff around on the underground). By road it's straight up the M3.
However, SEN is easier than LTN and STN.
LHR is on the doorstep, so easiest of all.
Average times now by train or Underground
Heathrow 45 minutes
Gatwick 58 minutes
Luton 1 hour 36 minutes
Southampton 1 hour 45 minutes
Stansted 1 hour 53 minutes
Southend 2 hours 2 minutes