Heater, lights, Api test kit , hydrometer if your on a budget or a refractometer if your willing to spend more. Of course you can use distilled, although it still might have traces of metal from the copper pipping it goes through. Ive personally used nothing but tap and dechlorination with no problems but its a gamble.
Most people on here are gonna tell you that you need the most expensive everything to have a successful reef, but from experience i started my 10 gal nano 9 months ago with not a clue about this hobby and so far put 180$ into it. I couldn't be happier with it.