Try local yacht clubs in the area that you are interested in - they always have the best value moorings available. There may be a wait at some clubs - but ask around first and you might be lucky.
A drying mooring in Teignmouth costs under £200 from Teignbridge District Council, Tel. 01626 361101, you can buy/rent swinging moorings on the Exe at Starcross, it is £500-750 as a one off cost and then the rent to Powderham castle which ( depending on LOA ) about £150 pa. Contact Starcross garage or Powderham estate for more accurate details. They have moorings for sale sometimes on the notice board at Starcross Fishing and Cruising Club. If you are fabulously wealthy you could go on the waiting list at Torquay, Brixham or Dartmouth marinas. To get a deep water mooring in Teignmouth you have to be able to trace your family history as Teignmouth residents to before 1066!
Good luck, South Devon is a brilliant place to sail.