There are a lot of people here with way more experience, but I'll share my .02. I was taught to quilt BEFORE binding, since the quilting process itself can 'draw up' the fabric a bit, which would then result in the binding not laying flat. So I'd say you're definitely doing it right.
As for how closely quilt lines should be spaced, usually the batting that I buy has guidelines on the bag or on the roll saying it should be quilted every 4 inches, or 5 inches, or 7 inches or whatever in order for it to be stable.
Hope this helps