we use bracklesham slip, its got a tractor that will do the launching for you, think its a £5 a day. You could use East Beach at Selsey but its a complete ball ache to launch, as its steep through shingle and the slip gets covered in shingle.
For sites to visit use Dive Hampshire and Isle of Wight and/or Dive Sussex. You can also dive Selsey Lifeboat station which is a pleasant dive in about 5m of water and can be pretty good.
theres Wittering Divers down there as well, so might be worth a call to them for advice and info.