I think the most popular materials for wipes are cotton fleece or velour or a soft terry. A lot of WHAMs make them, some with two different sides like velour and flannelette together, one side for grippiness (is that even a word?) and another for a soft final wipe.

I wasn't sure if I'd use cloth wipes so to start off with I cut up some terry and flanny flats and started using those. Once I knew I would use them I bought some to check out the different materials and sizes. Now I've just ordered some cotton velour and flannelette from an online store to make some myself, some with double sided velour and some flanny/velour combination.