Find Ancestors

Hi can anyone give me more info on the ancestral roots of John Palmer of Hartlip in Kent and His younger brother William of Snodland in kent.John is known as the father of Sir Anthony Palmer of Chilham and the west indies...later generations are known to have set up towns in virginia and pennyslvania.I have all this info already.....my quest is to find where john and william where born and why they are situated where they are...they must of come from a prominent family...my suspicions suggest from the wingham palmers as sir anthony uses their heraldic crest...though his father uses a 3 lions arg etc etc....though they may also be of the family of palmers from snodland who includes sir henry palmer of bekesbourne...known as comp controller of the navies and defender of guisness castle in calais.Henry is buried in bekesbourne...well a memorial stands anyway....