Traditional Irish Music
This is probably a question fiddle players should answer but since you haven't had many responses I thought I'd play along. I used to teach whistle at an Irish arts academy and it was always rough coming up with a syllabus that would give all academy students a set of tunes they could play together at the end of the term. The difficulty was apparent when I'd suggest "such and such is very easy to learn on the whistle" and the fiddle teacher would respond "ah, but that's a b*#$@ for a beginner on fiddle!"
Pick tunes that are easy for a beginner to finger/bow so that they can focus on rhythm and tone. Make it simple and enjoyable so that they won't get burned out on frustration too early. Don't bother with complex technique or ornamentation for at least a year or so. Ornamentation can always be added but it's no good without a foundation good rhythm and tone being established first. Pick tunes that expose them to different scales (i.e. one in G, one in D, one in Em, etc) and include a mixture of reels, jigs, etc.
I can't imagine there's a difference, but I learned by ear so I wouldn't be that knowledgeable about the way its done in classes. I see you're learning the pipes. My brother started about a year ago. Really is an amazing instrument!
At The Riley School of Music, the teachers usually start the very beginner fiddlers with easy polkas (children and adults). I agree with Tony about polkas. The very first polka is usually Britches Full of Stitches - started on the open "A" string. This is because the A and E strings are easiest for beginners to reach, especially if they are little children with small hands. After polka style is ingrained, next come jigs, maybe slip jigs too, then reels. Reinforce the rhythm patterns, since they may not be familiar with the Irish traditional rhythms. Hope this is helpful.
Swallowtail jig is also a good one