As stated, Ammonia is the killer, the thing to watch closely. Nitrite is a non-issue. I don't even test for it. It would almost be impossible for nitrite to build up to the levels in a SW tank necessary to impact animals. Nitrate should be below 20 ppm, and if you're keeping a reef it should be as close to 0 as possible.
When your cycle is finished, your nitrate will not be 0 as stated above. It will be pretty high, which is why you'll want to do some water changes. Over time, if you have sufficient live rock and you do regular water changes, the nitrate should come down.