Where do I start?
Strange as it may sound, the best place to start is to learn the dances.
The great Breton flute player Jean-Michel Veillon gives this advice, and it really is true: it’s hard to get the rhythm of Breton dance music until you know the steps. Then if you play with the steps in your mind, or even move your feet while playing (not so easy, for me anyway), you’ll settle into the correct rhythm naturally.
Many Breton tunes are deceptively simple and repetitive; they’re pretty easy to learn (and easy to forget), but 90% of the non-Breton players I hear playing them don’t have the rhythms correct because they don’t understand the dances. In most festou-noz (night dances that can go on all night long in Brittany), the players don’t even announce what kind of dance they’re going to play – the dancers can tell by the rhythm.
There are about 320 zillion youtube videos showing people dancing to various Breton dances, and watching them is one way to learn if you don’t have any opportunities to learn in person.
Other than that, listen to some recordings, slow them down if necessary, and learn the notes, then try to imitate the rhythm as best you can.
By the way, even though it’s largely about flute playing, many of the things that Jean-Michel Veillon says in this interview I did with him years ago would also hold true for playing Breton music on the whistle:
I visited the Breton fort holds in the west of Brittany all the way to the Breton shorelines this year.
I didn’t come across any Breton flute music at all. It was a bit disappointing. Nevermind - the internet to the rescue:
http://breizhpartitions.free.fr/en/flute_scores.php
There are some Breton derivatives here. Generally if you want to start with Breton music, try eating a black wheaten authentic Breton crepe first. It really whets your appetite for more of the fabulous culture of this region.
Breton dancing is a gas, and very approachable for total beginners.
Maybe not the kost ar c’hoat, though! 
There are a few others that are pretty acrobatic…a well-danced kost ar c’hoat is lovely to behold but I still haven’t mastered it myself despite 8 years of trying. (But I’m one of the world’s worst dancers)
Before I start digging into YouTube clips of _an dro_s and the like, which key of 'whistle should I have at hand?
The biniou koz (Breton bagpipe) and bombarde (shawm-like instrument) are generally pitched in Bb (bombardes are available in other keys, but I believe the biniou is now only made in Bb), so Bb is a good key for a whistle to follow along. That said, a D whistle would work for playing along with many modern Breton bands that don’t use biniou and bombarde.
My girlfriend is from Brittany and is a singer; she grew up going to festou-noz and dancing to biniou and bombarde, and when she started singing she fell naturally into the key of Bb. She had no idea what key she was singing in, but every time she started to sing I could pick up my Bb flute and she’d be right on pitch…that key was in her bones.
Dunno. But this (etc.) is where you could end up! 
Wow, it’s Briverdance! 
I spent a few days in Pontivy while my girlfriend was at a singing workshop, and it happened to be the same weekend as a national competition of bagadou (plural of bagad, a big band of Scottish bagpipes, biniou koz, and bombards with drum accompaniment that you see in the clip that Jem linked to). These are relatively recent inventions and are very popular in Brittany – I decided to go watch for a while, and sat in the back of a huge auditorium, but still had to cover my ears when the bands came out, it was ear-splitting.
I don’t think this is so easy to learn andro for example that is, with hanter dro and gavotte montagnes, the kind of dance you will perhaps learn first (that’s my case !) : you have to move simultaneously, and synchroneously, your legs AND your arms in perpendicular planes …
If you want to see top level breton dancing, have a look on the 2 dvd volumes of the Kendalc’h association “Apprenez les danses bretonnes”, available on sites such as the Coop Breizh one.
Depending with the kind of musicians you’re playing with !
I currently play with a box player which uses a C/G instrument. So, my D whistle and my Boehm flute are appropriate as our repertoire is in C or G. I can add a whistle in C (cos’ I’m not very fluent with the Fnatural fingering), but thus I have to transpose the natural fingerings (that is for example for a D : XXX XXO), that can be a little confusing (but a good exercice too !).
So far as digging up tunes, does anyone have some favourite YouTube links? The trouble with just searching “an dro” is that you get a zillion hits of people playing a tune called “An Dro” on some Carlos Nunez album.
Any recommended “you’ll hear this in every Breton session” tunes? Are most Breton tunes in some form of minor scale? Is it generally a Dorian or Aeolian minor?
Folks above mentioned the importance of knowing dance rhythm to playing Breton tunes, but are there any Breton forms with loser metre, and slow airs or similar?
There is a CD of Breton music played on wooden “simple-system” flutes, titled “Bro Dreger VIII - Flute Traversiere en Tregor.”
21 tracks by 11 Breton flute players.
A nice tune, imo is Fonn Briotánach: Jezaique from Paddy Keenans Port an Piobaire album. I don’t know how “genuine” it is og course, but a nice tune nonetheless.