That is so cool!

I would think that Ralphie is right on the money. Plus, if you have two banjos and a guitar, you would be looking at three pickups (unless you got one of those old contact ones and played around with it.)

A mic will give you some sense of "air" to the recording, just play around a bit for proper placement- on the guitar, you might want to try pointing it at the neck, not the soundhole.

Depending how much you want to spend, there are alarmingly good condenser mics available relatively cheaply now, although these normally require a pre-amp.(which, ART ones in particular, are relatively obtainable now too.) But yeah- renting or borrowing one is a great option.

Enjoy, have fun and don't worry about a few rough edges...that's what makes this music so enjoyable, the human feel.