Library Classification Systems

I have belatedly realized that part of the problem I've been having lately in finding things in my digitized collection of books is that I don't have a consistent classification system for them. Thus I often don't find something I'm looking for. This has lead to me getting multiple digitizations of the same book in my library, and not getting digital versions of other books I have in hardcopy.  (My eventual goal is to have a digital backup of every book I own.)

So, now I'm looking into library classifications so that I can give consistent call numbers to every digital book I own, and then find them again. To achieve this, I have a fair number of desiderata:

1. It would help greatly if there were an online catalog available so that I could look up the classification codes of all my books, rather than having to manually work through a rules set to assign them. The only one I know is the LCC (Library of Congress Classification) but there must be others.
   
2. I want the end results to be reasonably organized and handy for browsing through. This is a vote against the LCC.
   
3. I'm not about to pay a licensing fee to organize my books, so I need to use a system that is completely open. This eliminates both the Universal Decimal and Dewey Decimal systems.
4. Although its not necessary, I tend towards the idea of a faceted system as I have no trouble with books being in multiple 'virtual bookshelves' at the same time.

So far, given all of the above, I'm drawing a complete blank and so I'm still using my current ad-hoc system, but I'd sure like to get a bit more organized in my book classification.