Number one, use Prime. It's a dechlorinator that also converts ammonia (toxic) to ammonium (relatively safe).
Secondly, I'd urge you to consider getting some live plants. Duckweed or Water lettuce would be ideal as a floater- you'll have to thin it out regularly, but it will help get your parameters under control.
'Lucky Bamboo' is also great- Just make sure the leaves are dry. Only the roots have to be submerged. (The stem can be, but all the leaves have to be out of the water.)
There's one more technique I use when a tank is cycling.. Many members here have never heard of it, and a few might argue, but it significantly speeds up the cycling in my experience-
Add 1/2 tsp of sugar per 5 gallons to your aquarium with every water change. (I dissolve it in a cup of water and slowly
pour it into the filter.) You can begin to wean your tank off of the sugar regime when ammonia and nitrite in your TANK hit 0.