Iirc, my local library "buys" a copy of the ebook. My local library uses Overdrive, too, and on their ebook page, it lists how many "copies" they have of a particular title and how many of those are available or lent out, much the same way they do for paper books. When I checked the FAQ, it mentioned something to the effect of you can request/recommend purchase of specific titles but it needs to be available via Overdrive. I think you can go to
http://search.overdrive.com but so far, that seems to only list what titles are available in what library so it may not be very complete. I would suggest checking online ebook retailers (e.g. booksonboard, fictionwise, etc) since they seem to have the most complete selections. Search for titles available in Adobe PDF or Adobe ePub format. Chances are, those will also be available on Overdrive for your library to purchase.
Oh, and if you're going to be borrowing books from the library, don't bother with the Kindle. Just stick to Sony Reader. Less hassle transferring borrowed ebooks that way. The Kindle doesn't have native support for Adobe DRM protected formats, and Amazon has taken steps to prevent you from using ebooks with regular Mobipocket DRM (which currently encompasses library ebooks). Sure, there are hacks to get around this limitation, but going the Sony Reader route is less troublesome.