I've done this when we moved into our new high school, so I'll give you my $.02.

Alphabetically would be nice if you never had new music, but with purchases you have to either renumber them, or possibly shift your entire library over a spot for a new piece. With computers it's far easier to create a numerical label/barcode rather than keep it in alpha order. (You could alpha your existing library when you redo it and know that older pieces will be close.)

Our library is categorized by Concert Music, Marching Music, and Jazz Music. (S&E is a mess that we still need to get through some day...) The Concert Music titles at the JH are labeled beginning at 3000 I believe, HS I began them at 10,000. Jazz is like 5,000, and Marching is 1000 I think. I did that so at a glance I could also backtrack a piece where it fit just by the number. We have our library in charms, but an excel spreadsheet or through google docs would certainly work just as well. In our database we keep composer, arranger, publication date, price paid, performance dates, and sub-genre (UIL, Pop, March, etc).

We have filing cabinets at the JH still, but at the HS are using the MusicFilingSystem shelves/hanging folders. Keeps things neat and we can search quickly for what we need. I personally wouldn't do it any other way. We do also keep scores with pieces unless they're oversized. Still trying to find a better way for them as more music comes out in that format for us.