8 bit PNGs use an indexed color palette like GIF. If you want variable transparency, use 32bit PNGs (24 bit color, 8 bit alpha). If you don't care about transparency, use 24 bit PNGs.
If you have areas of solid, even colors then you may be able to get away with an 8 bit PNG, but you will likely need 24 bit PNG for reasonable color reproduction. 8 bit PNGs (or less) are optimal for size. 24 bit PNGs (or 48 bit PNGs) are optimal for color reproduction.
When I last used PSP, you needed to set the transparent color in the color palettes, not when you save the image.