Which type of connective tissue is found in the papillary layer of the dermis and contains all of the cell types of connective tissue proper?

That is Loose Areolar connective tissue within the "Papillary" layer, for good capillary blood supply to the basement membrane of the epidermis.

The underlying "Reticular" dermal layer contains much more collagen in its matrix, which is a dense, irregular type of connective tissue.