Whether or not you can get a "decent" camcorder in that price range, depends entirely upon your definition of "decent". That's about all I'll say about that.
Now, about your audio quesiton..
Most soundboards will have a "Tape out" with RCA connections. You'll need a cable with two male RCA plugs and a 1/8" male mini plug. Otherwise, look for "Line out" connections. These can be RCA or they may be 1/4" female. Again, you'll need the 1/8" male connector for your camera or audio adapter and the appropriate male connectors for the sound board.
You'll want to be aware whether your sound board is applying channel volume levels and equalization to your connections (preferably, it is). Which brings up another point - your soundboard now becomes your mixer. If the audio is not mixed properly on the board...well, that's what's going onto your tape.
It can be difficult to tell during a live session, just how to mix everything. That's why I prefer to mic choirs myself, using our own mics, thus giving me the freedom to mix in post.
When miking a choir, it is best to split them into soprano, alto and bass groups and set them in semi circles of three or four with a mic in the middle of each little group. Keep each group's recording separate so you can mix in post. You nearly have to pull a gun on the choir directors to get them to allow this, but you'll get the best sound. If you're doing an annual video, it will definitely worthwhile. If it's an every week thing, then probably not worth the hassle.
Whatever you do, be sure and mic the piano or organ. I know the other mics will pick it up, but you'll get a much clearer track on it if you mic it properly and have as much separation between this instrument and singers as possible.
Be sure your camera or audio adapter (like Beachtek, etc.) let's you set it to "Line" instead of "Mic".