Is this an enjoyable hobby that can keep my mind at ease?
I really like the more intricate Touhou and other otaku related papercraft I've seen, I hope I can make those eventually.
Is it good to just start with a traditional paper bird and work from there?
You are referring to two different hobbies in your post. Papercraft is not origami, and vice versa.
If you want to start papercraft, just choose a simple looking model and try it out (like a 1 or 2 sheeter). If you can't do it, just choose something simpler. If it is too easy, choose something harder.
For origami, either start with a website like
http://en.origami-club.com/
or look up books by John Montroll whom most of the people on here started out on (including myself).