I would like to find a cell which requires a small number of z-sections to image using high NA objectives. Thinnest refers to the z dimension of the cell over the cytoplasmic portion.
I would suggest using cells from a simple epithelium. PtK1, PtK2, or REF52 cells work really well for microscopy applications that require very thin pancake-like cells. See "Spatiotemporal Feedback between Actomyosin and Focal-Adhesion Systems Optimizes Rapid Cell Migration," Cell 2006 for some example images from PtK1 cells.