I have been to Barbados twice and still haven't found a nice beach there. I don't know if I'm going to all the wrong places or what, but I don't even particularly like Barbados at all. I don't know whal all the fuss is about, the taxi drivers (some not all) rip you off and the locals aren't particularly friendly (yelled at us for taking a picture of the town square) and very aggressive heckling by vendors and taxi drivers both at the pier and in town. Hope you have better luck. I can tell you NOT to go to the public beach next to the Colony Club hotel, that's where we went and it wasn't great.
Re Antigua, there is a nice beach not far from the pier. I can't remember the name of it but is is where the Sandals resort is located. The resort's beach isn't private so they share it with the public on this beach. Bars, waverunner rentals, etc. and very friendly locals and vendors that are not pushy at all.
Re St. Lucia, we didn't go to a beach at this island but our friends did and said it was beautiful. Wish I knew the name to tell you.