Hi Ed and Fran,
If you want to launch on your own without boatyard assistance and crane, I'd recommend the public slip way at Dell Quay, best to avoid on busy weekends when the sailing club are launching their dinghies and safety boats. It's also a great place to anchor and spend the night with a great pub by the slipway.
Other places I'd recommend visiting are Bosham (you'll have to dryout) and Emsworth (you can use the jetty, which does dryout at low water, for up to 4hrs but there's a fee) or further out in the Emsworth Channel in deeper water there's the visitors pontoon (I'd only recommend if you have a motorised tender). Both places have nice pubs and resturants. Emsworth is bigger and has supermarkets too. Emsworth is easy to get to on the train too and also has a public slipway.
Also, highly recommend beaching the boat at East Head behind the dunes, or nipping out of the harbour and sailing to Bembridge on the IoW.
Manuel Panzera
Galadriel - Parker 21