Yes, use the tap water. Watch new grows after first watering, if you see nuteburn next time mix tap water with your "filtered" water. I had highly nutrient soil, I started with deionized water. After a week or so, I used 1:1 tap:deionized. After a week or so, I used only tap water. They were just fine.

I'm not saying go buy PH pen, up/down solutions and other things which are not really necessary for a cabinet in the very first place.
If you want a successful grow you should have air change. Check for PC fans on ebay or local shops. They're cheap and effective for CFLs. You just need one or two PC fans an adapter to run them. If you don't afford $10 on them, you may risking all your expenses for this grow. I got my first fans from a second hand shop. 4 fans in total only for $5. And some adapters for them. Didn't cost more than $10 in total. This way I experienced and learned. Then went to a PC shop, bought better ones, and still I'm using them.

These can be found on ebay or local stores, good and effective for exhaust use and no light leaks. They called "system blower"
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