The C&C Club site at Pevensey fits your requirements and is right on the beach (peebles).
It is very popular so can get crowded.
Small shop on site otherwise you will need to drive to any amenities.
Quaint train halt nearby with trains to Bexhill or Eastbourne.
Crossing gates manually opened by Rail Track Staff on coast road to Bexhill, a step back in time!
Some train noise on sight but not bad.
Sovereign harbour towards Eastbourne at 4 miles) .... a marina with out of town shoping, pubs and boat trips is worth a visit.