I believe, here one basic input is missing. You define an strategy for a storage type and then using the storage type indicator (which is defined for a material in material master WM1 view) you define the search strategy.if you want to suggested putaway and picking for a set of material then define the storage type indicator in the WM1 view for only those material and define the storage type search for the Storage type indicator
Few query which is unanswered
1) why you selected strategy A, This is specific to partial quantity management
2) As per your business process where and how (here i mean expectation from system) they want to store those material for which system is not going to propose putaway and picking bin)