I first heard it in the late fall / early winter of 1976, I think, on an LP of Medieval-ish Xmas music of the British Isles and Ireland that I had in my home. It was played on a hammer dulcimer - those are Xmas-y sounding - and the track, the only one of its genre, was titled: "Ireland". That's it. Never mind that with a dulcimer the track probably should've been titled "Antrim", that Morrisson's wouldn't be Medieval, that it isn't an Xmas chune, that the compilers might have done better to choose the Wexford Carol (I didn't know any of that), and that the album was titled Christesmas In Anglia (that issue I knew well enough). I always remembered the tune ever after. Never did learn the name of it until about 1993 or so, which was when I finally decided to seriously start learning to play the music.
No, wait. Maybe not Morrisson's, but the Mooncoin Jig, and God only knows when I heard and learned that one. Could've been as early as 1973. It was on a cassette tape, probably on a portable tape deck, that I would have listened to in my car. I think. Oh, heck. I don't remember which came first. One of those two. But Morrisson's stands out the most as The Tune, although I caught them both in whatever order. And do you know, to this day I really don't play The Mooncoin.
"If you take music out of this world, you will have nothing but a ball of fire." - Balochi musician
My first was Down by the Sally Gardens. I played it all the time. Someone asked me if that was the only tune I knew. It was. I still think it's very pretty.
"Life is far too important to be taken seriously"
~Oscar Wilde
Same here as Tucsonwhistler - Down by the Sally Gardens. That would have been December of '06 on my first whistle, a Jerry Freeman Mellow Dog, which I still have.
"Those who can make you believe absurdities
can make you commit atrocities." - Voltaire
The first Irish tune I learned a couple of years ago was the polka, "The Rakes of Mallow." These old, gimpy fingers are still working on it and a few others. Great fun!
It was the Irish Washerwoman, which I learned to play on the harmonica I bought when I was 16, and knew because if there was one tune every American kid knew from Ireland back in those days, that was the one.
Interesting about Sally Gardens being probably a wide choice... I love teaching that tune as a first tune, especially to folks who might not have heard a lot of deep traditional repertoire but can get the concept of basic song phrase structure. And it just sounds good, too.
Believe it or not, I think Tabhair Dom Do Lamh may indeed be the first one I tried to pick out on the whistle--I was captivated by Planxty's version years and years ago (heard it on the radio, I think maybe even taped it on cassette and might even still have that cassette somewhere).
I've only gotten into whistling this past year, when I purchased a few cheap Clarkes for the kids' homeschool program last fall. The TinWhistler version of Give Me Your Hand really made me want to play it on the whistle. Probably the first thing I ever played on the whistle was a simple tune from the kids' lessons, like Twinkle Twinkle, but I do believe that your birth-tune is the first Irish tune I ever tried to figure out for myself. I still stumble at it, but I've been working it out ever since. (I soon found Ryan Duns' lessons and started with those.)
Yes, Mockingbird... and what an unusual wedding it was!
Barry Kern was a great square dance caller and a gifted carpenter. For his bride, Linda Higginbotham (just then starting to learn banjo), he built a 3-story treehouse that somehow had a functioning heating and plumbing system. Seriously. They lived in the woods on a little piece of land a few miles outside Bloomington, Indiana... the ceremony was conducted by Altha J. Cravey, a friend of the bridal couple and avid dancer, who read a poem; Altha is now a major scholar at Univ. of North Carolina I believe and writes books like "Women and Work in Mexico's Maquiladoras" and other topics of gender and immigration. After the poem Miles Krassen and I played two jigs as the wedding song -- Carraroe Jig and Portroe Jig. Then, it being February and a bit chilly in the woods, everyone went inside the cabin and ate and drank to our hearts' content.
July 3 ... My Tune-iversary!! 
