Mine are about 2.5 millimeters on a tenor top. You know, not too thick and not to thin. 2 mm is probably fine too. Not sure the thickness is terribly important... What is important is that the grain orientation is perpendicular to the grain of the top creating a ply. Strength is important here to counteract the tendency of the bridge to dip forward under string pressure and deform the top which can lead to changes in compensation and string height.
As for wood type, I'm not sure this is a big deal either. My thinking is that like should go with like since they will expand and contract more or less the same. Shrug. I have used spruce with spruce, mahogany with mahogany and myrtle with myrtle and it seems to work. I've used spruce with redwood and that was fine too. Maybe the main reason is that when I thin the top, there are handy thinned pieces of cut-off wood available which make great bridge patches with the least amount of work. My sneaking suspicion is that anything probably works fine other than balsa wood rubber and we can chalk this one up to OUBS (obsessive ukulele building syndrome) of which I am frequently guilty.