If you want to go via Lymington, take the Flyer down the branch from Brockenhurst, get off at the platform that is all that is left of Lymington Pier station, walk forward a few yeards into the passenger terminal. With any luck the ship will be there waiting..you have to get on via the loading ramp. At Yarmouth you get out through the side. You then have to walk past the ticket office, and then turn right and cross the access road. There is a bus layby with a ticket and information kiosk where you can purchase a rover ticket. The bus to Newport runs from there and there's also one to Alum Chine. At Newport you have to change at the bus station to get to Ryde, Cowes, Ventnor, Shanklin..
The East Cowes ferry used to stop off at West Cowes on occasions and then cross the Medina River to East Cowes but now it just goes to East Cowes. You then need to take the chain ferry which I think is still free for foot passengers. There is a midi-bus to Newport from the terminal at West Cowes.
The free blue bus to Town Quay leaves from Southampton Central south side and drops you off at the ferry terminal and then runs on to the Red Jet/Hythe Ferry office which is in the building complex on the quay. The ferry takes much longer than the Red Jet but you have the refreshments on board! Before licensing hours were relaxed you could get an alcoholic drink on board way before opening hours...same as on British Rail.