An established tank should be tested for pH, alkalinity, calcium, and occasionally nitrate and phosphate. I usually only test the latter two every month or so unless there is an algae bloom or some such. You should also have an ammonia and nitrite test on hand, these tests are needed when your tank is cycling and also useful to know when adding livestock that the bioload isn't too much for your tank.
As to the proper levels...
alkalinity 2.5-4.0 meq/L or 7-11 dkh
calcium should be around 380-450ppm
ammonia, nitrite, phosphate and nitrate should all be undetectable.