There is no such thing as an audio interface geared for an accordion, the first and most important factor is your budget. The more you pay, the higher dynamic range, the greater gain and lower noise you get.
That said, this is a nice time to be an accordionist that wants to record, you can get some fairly decent audio interfaces for fairly reasonable prices. The low end starts with ones from Behringer, midrange ones come from Focusrite and upper ones come from names like Antelop, Audient, etc.
I have a bit of a small home studio and currently have 2 audio interfaces, one that is portable and one that's more of a true full size mixer.
My first one is a Zoom F4, made mainly for cinematic purposes, it is a 6-input unit that can record at up to 256k (massive overkill for us), but is amazingly low noise and has a ton of gain and can be AA-battery powered as well as 12-volt or mains powered..
My second one is a Mackie 1640i 16-channel mixer that is a true 16 channel in and 16-channel out Firewire audio interface that can literally record 16 channels all at once in to a DAW and is a really nice mixer with very low latency (think single digit latency). It's claim to fame is that its super clean and when plugged in to a computer, you can use VST plug-ins to augment the sound coming in and/or out.
What will have greater impact is if you want to record an acoustic accordion is choice of microphone... that's a world all unto it's own.
If I had to choose budget equipment but NOT want budget sound, I'd get something like a Behringer U-PHORIA UMC202HD, 2-Channel a pair of mic stands, 2 XLR cables and a pair of Neewer NW-410 mics. Shopping carefully you are easily under $300 and to get better results you would have to spend upwards of $600US to improve on it.
I own the Neewer NW-410 mics and they're not only cute, but really sound good for a pair of mics with 3 different exchangeable heads. They are condenser mics, so they must be powered by phantom power.
I also own a pair of super cheap Newer NW-800 mics that go for $20 each, and though nowhere near as good as the 410's are the best super tiny budget mics on the market.
Of course I also own a matched pair of SE Electronics sE4400a mics but they are not budget mics. At $1100US these are one of those little known gems in the audio recording world that have a sound capturing ability that if you want better, need to spend 3 times more. A very neutral sound.
Buy 2 mics, you want a stereo image... the 1940's mono sound is out, unless you want that kind of result of course!
