Along the Solent Way
Lymington Town Station
Lymington is a branch line off the main railway line, London Waterloo to Weymouth. The line is single track and has 2 stops, Lymington Town (5 minutes from the town centre) and Lymington Pier (for the Isle of Wight ferry).
You can go to the Isle of Wight from here and buy a ticket that takes you to Lymington Pier station and also includes the ferry trip to Yarmouth.

Rail timetables
lymington railway map
Picture showing the walk from Milford on Sea to Lymington The Solent Way map