Q: How does one collect gray water to use for watering plants? Or more to the point, what already-used water is safe to use?

A: My definition is that gray water is that that is collected from bathroom sink, tub, shower or clothes washer. Water from toilet or kitchen sink is “black water”.
One most easily collects it with a bucket in the shower/tub. You could conceivably change your plumbing to get more water from the other sources but you need a permit to do that.