The length of time for ammonia and nitrites varies--it will not occur in a set number of days. And, they are good to have to test the water in case things start going screwy. Nitrates, unless you have a heavily planted tank, will be present in all tanks but those with very, very light stocking and frequent water changes.
I consider pH, GH, KH, ammonia, nitrites, and nitrates to be essential for most tanks. Phosphates can be useful if you have algae concerns.