Welcome Trip,
You’ve come to the right place. As one who is not that far removed from newbie status (not quite 3 years) and whose practice situation is not all that different from yours, I’ll tell what worked for me, and didn’t. Some of the more experienced will add to this I’m sure and may have differing views. This is what keeps this board so lively and fun IMHO.
First, get one whistle that is in tune with itself and the world and make that one the only one you play at first since you don’t want to deal with the idiosyncrasies of different whistles at this stage. What I mean by that is beg or borrow a tuner, or find a web based one, to insure that when you play a D it is indeed a D and that you can control the flatness or sharpness comfortably with your breath or by moving the head or tuning slide if available. Then make sure that each note in the first two octaves is in relative tune with the bell note (D) and which ones you have to blow harder or softer to attain. Make sure you warm the whistle, (mainly the head until you get to low whistles which may require more warming) before playing by blowing a few times through the head with the window covered or hold the head in your hand or under your arm to warm it.
Choose three tunes, one each designed to play slow, medium and fast. Do not try embellishments or ornamentation such as slides, cuts, rolls etc. until you can play the tunes through without mistakes. Break down the tunes into parts so that you can practice in short intervals. It is much easier to learn short passages perfectly, then join them together to make a complete tune. Then finally begin to add your own personal ornamentation. This practice will make you solid with your fingering technique.
The most difficult thing to learn will be breath control. As you noted with the whistle that started off in the second octave, this will be the biggest difference between instruments. Practice each note slowly by starting off blowing as softly as possible then gradually increasing pressure until the whistle jumps to the next octave and remember there are three of them possible (though the third is rarely used and may sterilize cats in the vicinity). This practice will be of tremendous help when you want to convey emotion in your playing and will be essential to play in tune without missing notes. You should try to play without tonguing except where a note requires same or for emphasis. You will discover that on some notes and some whistles you will want tonguing to quickly change notes since some instruments are more responsive than others and not always on the same notes.
If I were to have 15 minutes, I’d spend it on one tune by working on the individual parts. Play them slowly through at first, then increase speed to the point where mistakes creep in. Practice just below this point on fast tunes. As you gain experience, practice at the final speed intended before beginning to add ornamentation. Then you may need to slow down again until these changes come automatic. I always start off any practice with a couple of scales, then a few intervals (thirds, fourths, fifths, up and down) which should take no more than two or three minutes at most. Scales are not a waste of time but I wouldn’t put much emphasis at all on them other than to help get used to the instrument and in the beginning they will help you learn to quickly make transitions.
And spend a lot of time listening to the pros on videos and recordings. It is amazing how much this will help. Also, although the tabs are sexy, they will eventually slow you down and are often wrong or incomplete.
There’s a lot more but this is how I started and it seems to have worked out very well. I could hold my own in sessions and when playing with other musicians after about a year with this routine.
Keep us up to date on your progress.
ecohawk