If you like the two Amede's, we're on the same wavelength. Also check out Octa Clark and Joe Falcon. I think all beginning players should listen to Nonc Allie Young. He wasn't the best technical player out there, but he was good, and had great rhythm, and his playing is easier to pick out than some.
Bal Chez Belizaire, if you can find it. It was recorded at his house by Gerard Dole, just Nonc Allie playing accordion, no accompaniment. Not sure how available it is.
There's also a recording with Ray Landry, that I can't recall the name of. And another with Cabri Menier called "Two Steppin with Nonc Allie. He also recorded some with the Balfa Brothers.
Sorry, not much help, all his recordings may be hard to find, if even available. Wade or Neal, y'all know of any?
Here's the one with Ray Landry.
In terms of early classics, you certainly want to pick up Iry LeJeune's "Cajun's Greatest: The Definitive Collection." IJ was the leading (accordion) player of the Cajun renaissance of the late 40's / early 50's, and between his material and Amede's you can build a great foundation for Cajun jams. Sadly, there isn't a great deal of recorded material by either, as both died young.
I'd heartily second Bryan's suggestion re Allie Young, and in particular the "Bal Chez Belisaire" CD he mentioned - not fancy, but clean accordion playing, very well recorded, and at a speed that you can keep up with. In the same vein, I'd suggest listening to Nathan Abshire -- again, very good accordion playing without too much ornamentation and at a manageable pace.
Finally, Valcour Records brought out an excellent CD early this year called "Cajun Accordion Kings (And The Queen)," produced by Steve Riley and Joel Savoy, which features new solo accordion performances by most of the leading older-generation Cajun accordion players alive today (it's light on younger [i.e., < 50] players). The CD is terrific, and Valcour has also put up a YouTube channel with videos of all the performances. Link to that channel is:
I do believe the "BASSMAN" nailed it down with those suggestions. Iry Lejeune, Amedee Ardoin, and Nathan Abshire. LOL, some of the hardest to play along with accordion players in history! But if you can play along with them tit for tat, then you're probably one of the best accordion players walking the earth today...LOL second to me of course.
Don't stop there, delve into Aldus Roger, Austin Pitre, Joe Falcon, Amede Breaux, Blind Uncle Gaspard "Rabbit Stole the Pumpkin", Angelas Lejeune if you're feeling brave enough. And last, but not least, when you're done with all these old players, take a stab at following Clifton Cheniere with the "C" accordion, or play his style in what ever key you can swing his style in. Clifton will teach you how to put your soul into your got dam accordion playing and singing.
All great suggestions so far. For another history lesson (and whole bunch of great music), try Neal P's site.
Neal is a Bravenet also.