Using autoclaved store-bought distilled water for labwork? I'm a high school student who's working on a molecular biology project in my school's lab. I need pure water for making culture media, buffers, running a BCA protein assay, running digests, cleaning glassware, etc. I don't have easy access to any professional lab equipment, so I'm looking for an easy way to get "lab-grade" water. Ideally I'd go to a university and fill up a carboy using a lab's milli-Q system, but this is not easy for me. I also don't want to shell out $$$ to buy ultra-pure water from online suppliers. Will autoclaving store-bought distilled water (NOT mineral or spring water), suffice for microbiology labwork that needs pure water?

Yes, distilled water would be absolutely fine for your needs. You really don't need ultrapure water except for the most sensitive of applications. You also don't need to autoclave the distilled water before making things like media/buffer/etc; instead you would autoclave/filter them after you make them.

You can take a look at this document for an overview on different grades of water.