All three have fabulous beaches. No such thing as "best".
St Thomas options include Maegens Bay (very beautiful VERY popular, full facilities).
Other options Coki Beach and Saphire Beach.
Antigua literally has 365 beaches. Hard to tell you "best".
St Lucia also many nice beaches. There is a public park north of Castries that has a great beach and the beaches in the area of the Rex St Lucian (also north of Castries) are public, nice and have facilities.
Suggest you get a Fodors or Frommers Caribbean guide . Both list beaches by types of activities , facilities etc.