Hmm.. I assume it's the initial cycling period going on here... tap with de-chlorinator is fine of the bat.. You'll need to do a good 50% water change at the end of the cycle anyways..
I've used that method in a pinch and things went fine..
Distilled (make sure it's RO
) from the grocers is fine..
The main reason behind not using (or the preference to not use) tap water is due to nitrates or phosphates (mostly) in the water.. There are also other undesirable trace elements there (copper, lead..who knows what..).
The main reason to not use tap is it lends to algae growth.
At a dollar+ a gallon for store water, it adds up in the long run...
But considering the tank is only 12g, I'd say it fits well within the normal budget and should work out fine (again, make sure it say reverse osmosis distilled on the label).
Just be sure to salt the water a day in advance and have a powerhead aerating it..