My way
I store my stamps by country, and I use the Leuchtturm (Lighthouse) Vario stock system. This works fine for me. Arranging and mounting my stamps by species requires too much work for me with the scope of my collection. But my interest is in the birds. Therefore I would like to see my birds on stamps presented by species in zoologically systematic order. I do, however, find arranging and re-arranging my birds in my database a good substitute.

Getting information
Beeing a member of a birdstamp society is a must if you want to stay informed on all aspects of bird stamp collecting.
Aves Philatelicae Scandiae
This is a link to a page written in Swedish. From APS you will receive a journal, Swedish, Norwegian, Danish, 6 times a year. New stamp issues are presented in Norwegian/English.
The Bird Stamp Society
Chris Gibbins presents an excellent introduction on this page at his Birds of the World on Postage Stamps website.

New issues
These are my main sources for information about new bird stamp issues
     New issues service from stamp dealer
     Journals from APS and the BSS
     Gibbons Stamp Monthly
     Michel Rundschau
     Yvert & Tellier Catalogue Supplement
and on Internet
     Linn's Stamp News
     Birds of the World on Postage Stamps