If somebody with no Arpitan heritage wanted to learn the Arpitan language, which dialect of Arpitan would you recommend that they learn?

All other things being equal, I’d be heading for a dialect that has had significant literary production (so you can find things to read in Arpitan), and a dialect that still survives to at least some extent (so you can at least theoretically find someone to talk to in it).

I’m biased, as my bio shows, towards the Val d’Aosta. But honestly, I don’t know another region that will satisfy both. Franco-Provençal has been dead in French Switzerland for two centuries, and is not doing that much better across the border in France. Its status in the Val d’Aosta is kind of artificial, and certainly much confused with the status of French; but it is still much healthier there than anywhere else.