I think my basement might be less than 60f (root cellar), my fermometer says the bucket is 59 and I just added more ice to the swamp cooler. It is bubbling away happily. I would say that is the perfect temp for many, many ales. As was mentioned, it is a bit warm for a lager.
The yeast you buy should have a range listed. My latest practice has been to cool to 5*f below that range, pitchy yeast, and let it warm up into the low end of that range over 12-24 hours, then hold at that temp for a week to 10 days. It works well for me. After that I pay a little less attention to the temp, knowing it won't rise much in a swamp cooler in my basement.