Cacti are the most problematic group of plants that we work with in terms of taxonomy and naming conventions. We typically make decisions on a species-by-species basis using a number of sources, including our own personal experiences. In general, we start with:
Anderson, E.F., 2001, The Cactus Family: Timber Press, Portland, OR.
Then we start making decisions on how we want to handle the genus-species assignments. We reject a number of the lumped genera, especially Lobivia and Eriosyce. For certain genera, we use separate resources. For example, for Copiapoa, we generally use (and reconcile):
Charles, G., 1998, Copiapoa: The Cactus File Handbook 4.
Schulz, R., 2006, Copiapoa: Schulz Publishing, Teesdale, Australia.
Schulz, R., and A. Kapitany, 1996, Copiapoa in their Environment: Southbank Publishing, Australia.
Two other useful books are:
Pilbeam, J., 1999,Mammillaria: The Cactus File Handbook 6, Cirio Publishing Services, UK.
Pilbeam, J., and D. Bowdery, 2005, Ferocactus: The British Cactus & Succulent Society, Hornchurch, UK.
Pilbeam, J., and B. Weightman, 2006, Ariocarpus et cetera: The British Cactus & Succulent Society, Hornchurch, UK.