For very delicate skins, you can't do better than aqueous cream - the sort used for eczema - which is pretty cheap from pharmacies. And you can't beat Vaseline as a lip salve and a night cream for when your skin is extra dry.
The best thing you can have in a face cream is an SPF to protect your skin from ageing. After that, ti's a case of finding one with a texture and scent which suits you.