Practicing schedules having been fully addressed I thought I might suggest what to practice 
I used to do a lot of teaching (private students, workshops at festivals and music camps) and a common thing I would have to get people to overcome is tonguing.
“Legit” musicians, fluent sightreaders, interpret the plain notes of standard written Irish Traditional Dance Music to mean that each note should be tongued. So I would hand out music with “ties” indicating legato playing, which helped them.
With some people the tonguing habit was very hard to break. With a couple people the only way I was able to get them to not tongue was to have them play while holding their tongue against the roof of their mouth. This created an “aha!” moment for them- they had no idea until then that they were tonguing every note.
Why do I think it’s essential to start out absolutely legato? Because tonguing the beginning of notes is a crutch which disguises both sloppy fingering and poor instruments.
Say, for a basic example, you’re going from G to B
xxx|ooo
xoo|ooo
but you’re inadvertently putting an A in between
xxx|ooo
xxo|ooo
xoo|ooo
which I can detect by watching your fingers, but isn’t heard because you’re tonging and the whistle is silent during the inserted wrong note.
Playing legato reveals all.
It gets harder to avoid inserting extra notes the more fingers are involved, say going from D to B
xxx|xxx
xoo|ooo
With instruments, I’m evaluating a pile of Low Ds right now and some have such stiff intransigent high notes that the worst, High B, can only be sounded by tonguing. IHMO such instruments are unsuitable for ITDM.
Also these “classical” players were in the habit of sneaking in breaths between eighth-notes, and had to be shown that in ITDM you create a breathing-spot by leaving out an eighth-note in a certain idiomatic way.
Because almost no written-out ITDM is arranged for specific instruments whistle-players must learn to be their own arrangers.
Or you can avoid the sheet music issues by learning entirely by ear. When I had beginning private students I gave them the option of going the sheet-music route or the traditional ear route (which many “classical” people are familiar with, the Suzuki Method).
The traditional Irish pedagogy is for beginners to learn through tunes. They generally start with jigs, then work up to reels. Since the vast majority of session time is spent playing jigs and reels this makes sense.
Non-trad “legit” pedagogy is for beginners, and seasoned players, to play exercises. Since at a gig your music stand often has a piece that you’ve never seen or heard before and you’re sightreading it cold it’s not much use practicing tunes, rather, you’re practicing skills that enable you to play anything placed on your music stand.
I’m in the middle. I think exercises are very useful for building breath-control on whistle or flute, say
D E D F# D G D A D B D c D d D e D f# D g D a D b (every note on-pitch, and absolutely no tonguing!)
Going legato from Bottom D to High B and back means having a whistle than can do it, and really knowing how to blow that whistle.