One of the determining factors is the stye of Louisiana music you are going to play.
At the risk of making overly broad generalizations, those playing traditional Cajun music tend to use external mics, and those playing zydeco generally use internal mics.
There are definite differences in the sound. The external mics have what I would call a clean, uncolored sound. You might call it a natural sound. The internal mics have a more gutsy growl, somewhat reminiscent of a blues harp player blowing into one of those bullet mics.
Internal mics are somewhat more convenient to use because you just plug in. With external, you have to mount it and then plug in. They sometimes get in the way, or fall off at the most inconvenient time (like the middle of a song).
Internal mics are less prone to feedback problems, and that is a HUGE advantage.
I have used both, but I now use internal exclusively. I like the sound and the feedback control.
The type of mics for internal or external use are typically a mic element from a dynamic mic. A condenser mic can be used externally, but must not be used internally.
The classic mic is the Shure R-65, which is the mic element from a Shure Unisphere. I have a couple of those. I have also used a Shure SM-57 element. On the recommendation of Big Nick and others, I have swapped out the Shure mics and use an Audio Technica DR mic element.
Here's a couple links to Big Nick's website which has come excellent info to get started on mic'ing:
I agree with everything Dave says. I use an internal mic on my Bb accordion (my zydeco box) and a clip on (audio-technica) on my C accordion. The clip on mic (which requires phantom power) is much brighter and louder than an internal mic. The internal mic also has the property of magnifying the sucking sound the accordion makes when you pull the bellows open.
You can fix the sucking sound of the internal mic by adding a foam windscreen around it. I have used a piece of nylon stocking, which also helps. I picked up that tip from someone on this board, but I don't remember who. It might have been Dana Mandell, who hasn't been around much lately.
You also play around with the direction that the mic is pointing inside the bellows. For reasons of minimizing feedback, it helps if the mic is pointing in towards your chest/stomach. If you do that, it also happens to not be pointed directly toward the air hole, so it helps with that problem at least a bit.