For cleansing foam, I am not quite sure how to recommend you as all the brands that I've used, I've no side effects, itchiness, dryness or whatsoever. But do find a cleansing foam that is compatible to your skin type. If your skin is dry, then get one which is suitable for dry to normal skin. If your skin tends to be oily, go for cleansing foams which is meant for normal skin to oily skin.
Here's how you should use a cleansing foam. Put/pump onto palm and make into bubble on palm before applying it on the face.
Maybe you can try the ones I've used below. My skin tends to be oily at times and the foams that I've used so far are so good. (top to bottom : Biore Facial Foam; Eversoft Facial Cleanser; Neutrogena Deep Clean Facial Cleanser)