Some great tips, Eagle.

The usual tip to get a tutor goes without saying, but since you mention that you are only in it for "personal intertainment".....here's one reason I find a real person invaluable: with so much going on -- fingering, air pressure, posture, rhythm, etc, etc. -- it really helps to have someone suggest what to focus on and to praise your progress on individual elements even when the overall effect can be discouraging.

Also if you plan to hold off on switching to the pipes, you'll want someone to help you select new tunes when you've mastered the tunes in the tutor itself.

As for fingering itself, there are lots of flexibility exercises you can do while you are sitting around doing other things in your life.

Watch for tension in your body....it has a way of radiating to your fingers making relaxed, but precise movements challenging.

Pay attention to where your fingers cover the holes. Eagle's tips are spot on. Start with the thumb and pinkies (as Eagle points out) and then see where the other fingers end up naturally. Everyone's fingers are a little different, so this is one you need to work out on your own then be conscious of what it feels like when the notes are clean. I find that I can "feel" a good performance by the airflow on my fingers.

Something I've never actually tried, but you might be aware of from your sax work, and that might help you enjoy playing tunes on the Practice Chanter is circular breathing. Since pipe tunes are designed to be played without stopping, using the continuous airflow of the bag and the background of the drones, breathing can be a challenge.

And finally, you can use your computer, smart phone, or tablet to record your playing. This can be really discouraging at first, but you'll appreciate your progress.