First day covers are simply a stamp used on the day it was first issued (or with a cancel saying this; these days they can be created for few months after the issue date). Most often the covers have a "cachet" - additional artwork. There were/are a number of large scale producers, many smaller producers, as well as amateurs who create their own covers for their own enjoyment. They can be collected topically, alongside stamps, or with a focus on a particular cachetmaker or stamp issue. For example, I collect as many different varieties as I can of first day covers of the 1953 Ohio Sesquicentennial stamp and several others. I also have a collection of a first day cover for each stamp issued in Ohio, and I collect cachets done by William Wright in the 1940s and the 1950s. Some collectors frown on first day covers as souvenirs made for collectors. Most of them are indeed that, but I thumb my nose at anyone who thinks first day covers are beneath them or the hobby. Collect what you enjoy!
Since you enjoy birds, I would encourage you to look for cachet work by Curtiss Poorman, who has done some remarkable hand-painted work involving birds. Sometimes they can be found affordably. You might also enjoy finding as many different covers as you can of the 20 cent blue jay stamp, etc. James McCusker has a large online selection of first day covers. You can frequently find things cheaper on
ebay if you are patient, but it's a great way to see what's out there and available.