Sailing academy on old Portland Naval base has excellent slipway and facilities:
www.wpnsa.org.uk/dayfees.htm - expensive (£21 up to 20ft) but showers, cafe, flushing facilities are worth it. Parking included, overnight secure when it's not busy included if you talk to them.
Bluewater Horizons at Ferrybridge launches with thier own tractor (£15 last I heard)
Both access Portland harbour at all states of tide, although race through Ferrybridge can be tricky.
Castletown - used mainly by dive boats, not sure of charges, if any.