I attended an appleseed course that some people have mentioned, and it helped me. I wasn't new to shooting, but I'd never had any kind of formal instruction. They don't teach really anything revolutionary (no pun intended—they talk about Revolutionary War stuff), but the guided practice made me more conscious of what I was doing with my body, my breathing, my eyes, and my trigger finger.
I don't think anyone answered your question about precision vs. accuracy. Not sure how you define those words, but to me, precision means tight groups (regardless of where they are on the target), while accuracy means hitting near the bulleye (even if the group isn't especially tight). Based on those interpretations, I'd say a new shooter who's practicing should be concerned with precision first. Until groups are fairly small and consistent, it can be hard to adjust the sights for better accuracy.
The shooter is responsible for precision.
The sights/scope deal with accuracy.
...that may not be true at longer distances when you're dealing with wind and significant bullet drop, but at 25 yards, I think it's a safe statement.