You could save money using RO water instead. Glacier Water has vending machines around So Cal that charge 30 cents per gallon for water that is virtually distilled quality. The stuff I buy measures around 6.6 PH. and very low GH/KH.
The pure distilled should measure right at 7.0 (I think)
I agree, it's going to be around 6.5-7.0, with of course close to zero GH/KH. It depends on how pure it actually is...any specific reason why you are going to use distilled water?