If the local shop operates on donations, and is a non-profit, that's probably your answer right there!
If you're really interested in cycling, these places are pretty much gold mines for people with little knowledge and little $$$, or any combination thereof. They also tend to attract people who just love cycling. I knew a bit about cycling before finding one (Recycle Ithaca's Bicycles in my case). I volunteered for a while, did a build-a-bike course, volunteered some more, and then I was hooked.
Talk to the director/coordinator, and let them know you are interested not only in cycling, but also learning about bikes. Also see if they have a repair class or series you can join.
As for a bike, I would recommend a hybrid. It's basically an upright road bike- faster than a mountain bike, but more comfortable (and less intimidating) than a road bike. You're looking for something that fits the terrain you are looking to ride. You will need gears, and you will get used to using them.
Once you've met some of the local cycling community, you'll have plenty of opportunities to learn.
