Water
 

I'm new to hydroponics and still doing lots of research before starting. I am thinking about doing a DWC or a drip irrigation with a 5 gallon bucket. Which water would be best to use? I know I see alot of websites suggesting using RO Water if possible, but what about distilled or purified water. Like the kind you can get from walmart either in gallon containers or in 5 gallon containers.

Distilled is just as good as reverse osmosis water. The main thing is that you want pure water, otherwise the materials it contains will throw off your TDS measurement and can make controlling pH more difficult.

Reverse osmosis and distilled water are basically pure water. "Purified" water could be distilled, R/O, or processed in some other way which may leave behind more than just the water. If the purified water is cheaper than the R/O or distilled, it would be worth picking up a gallon to check with a TDS meter. If it's not usable for your garden, at least you can drink it. :)