Kai Kecil - island with the best beaches in Indonesia. White sand, high palm trees and almost no tourists, - it's a best recipe for a tropical paradise. Keep in mind that in 1999-2003 there was a civil war between Muslims and Catholics. Now only segregation reminds about that. There are purely Muslim or purely Catholic villages. Almost all of the best beaches are located near the Catholic settlements. Shore and seabed: sand. 
High season on the island is the period from June to August, when it is relatively cool and no much rains. The worst time to visit the island is the rainy season from November to April with the peak of rains in December-January.