Maybe it's because I've played since I was really young, but I don't think there's anything as "Irish fiddle music" in such a distinct sense. It's really fast and imposing at first, but you realize that it's fairly easy to play if you just stick with it. But it's sort of like getting good at certain composers' material. You don't study Bach specifically, unless you're at a really high level. Even then, that's just to give a select few players something to do.

If you haven't played violin before, then any basic lessons will do for a time. You wouldn't learn anything differently, I wouldn't think - unless some fiddle player completely shuns written music or something. And I'm guessing they don't care about form, but you should early on. Fiddle players hunch like no other, but they kind of earned it by playing for a while and deciding it works.