If you are dosing 2ppm ammonia, and 24 hours later there is 0ppm ammonia and nitrite and your nitrates are rising then you are cycled and you can add fish.
I would be a little concerned about the 0ppm nitrate. Did you do a water change just before doing the test? Are you sure you did the nitrate test correctly? (Assuming API liquid test kit, you have to really shake the heck out of bottle #2 or you get false 0ppm reading). Is your tank planted? That might explain where the nitrate went.
If you are happy with the ammonia and nitrite being 0ppm, then i would start stocking, lightly. Keep up with daily testing, if you get a spike, 25% water change.