Speaking for the 12th century, spindle whorls were made of a variety of materials including chalk (I have made an exact replica of one such using chalk from Dover Cliffs), lead, wood, copper alloy, pottery and various types of stone. An example found at Chester is of cow leg bone. It is interesting that in almost all contemporary depictions, however, spinning is being done without any weight on the spindle, which I am told is perfectly possible in some situations. The spindle itself was often made from the wood of the English spindle tree, which will not splinter or split in use (there are several of these trees in hedgerows within 250 yards of my door). Dogwood also makes very good spindles.
No upright spinning wheels at that time in history, not sure when they appeared but I guess its widespread use was post-medieval (modern era). Here is a 12th century Norman woman spinning without any weight on her spindle, taken from the Fecamp Psalter of around 1175. The distaff is an essential element of the process:
This is a clearer depiction from the English Hunterian or York Psalter of about the same period, again without a weight on the spindle and with the very prominent distaff: