Many folks recommend distilled over "drinking" water just 'cos you don't know what's been removed, or remains, in the drinking stuff. Calcium and Magnesium are the two big concerns I can think of.

pH strips are very accurate. You just gotta be able to match the colors! I've got some that are sensitive to trace amounts of chlorine, but they only indicate pH down to 6.2. You'd probably want some that'll read down to 4.5 -5.0 or so.

Skip the soil meter. If you find one that actually works (doubtful) it will cost $$$. Just check the pH of your runoff with strips or meter/pen.

Milwaukee 600's are available on ebay for about $20. I got an aquarium meter that's rediculously accurate for about $20, too.

pH controls lotsa mechanisms within your plant. A very obvious one is nutrient uptake--certain nutrients are absorbed best at certain pH's. If your pH is too far outta whack, you can have "lockout," which means you've got nutrients there that the plant can't use. It looks like it's starving, but adding nutes makes everything worse...

"pH balancing" distilled water's a bit tricky, though. (Gotta add all your stuff first.)