Traffic off Hayling is at its worst late on sunny Sunday/Bank Holiday afternoons when the whole world wants to go back to London and points north. It can back up almost to the seafront. Get your timing right (mid afternoon or late evening) and it is not too much of a problem.
As t'other Roy says Northney (not Langstone) marina is a good launch site. I believe it is £8.00 each way or £165 p.a. for unlimited launches. Very handy for Havant Tesco, which sells the cheapest petrol around here and being close to the bridge, bypasses most of the traffic jam.
There are nearly 9,000 (yep, nine thousand) swinging moorings in Chichester harbour and they all have a boat. Some belong to sailing clubs, most belong to the harbour conservancy, and some are private. Have a word with the harbour office.
Eastney Cruising Association (ECA) is popular with several RibNetters. They have boat parking and the slip is right in Langstone entrance, much closer to the solent & IOW. I am sure someone will fill you in on that side of things.