Michael,
Welcome ! to both the Forum and the Eastern Catholic Churches.
You asked for reading materials. I agree with John S.' and others' recommendations. I would also suggest the following:
(1) Light for Life.
It's an anonymously written work for the Eastern Catholic Churches. It summarizes beliefs, practices and spirituality. It is a *very* good summary: concise, accurate and deep. It's a three-volume set of slim, readable books. (Don't be put off by "three volumes"-- together, they would make one ordinary sized book.) You can get it online from the Byzantine Catholic Seminary's website at
http://www.byzantines.net/byzantinepress/theology.htm (toward the bottom of the page).
(2) Anything by the late Archbishop Joseph Raya. I don't agree with every word he has written, but he is a well-regarded author by me and by most Eastern Catholics. I would start with his "Abundance of Love." You can get it at Theobooks at
http://www.theobooks.org/index.asp?PageAction=VIEWPROD&ProdID=810 .
The Orthodox Church (by Bishop Timothy / Kallistos Ware) offers a very good summary of Eastern Christian history as well as Eastern Christian beliefs.
The Orthodox Way (also by Bishop Kallistos Ware) offers a very good, in-depth discussion of Eastern Christian spirituality. Keep in mind: these books are written from the perspective of the Orthodox Church, not the Eastern Catholic Churches. The Orthodox and Eastern Catholics are similar, but there are real differences that stem from the Eastern Catholics' acceptance of the pope. Nevertheless, Eastern Christians (Orthodox, Eastern Catholics, non-Chalcedonians) have a lot in common in theology, spirituality and heritage. For a good introduction all of Eastern Christianity, see
"The Eastern Christian Churches" which is available for free online at
http://www.cnewa.org/ecc-bodypg.aspx?eccpageID=3&IndexView=toc .
Finally, visiting this Forum can be invaluable for learning more about Eastern Christianity. Its members are generally very committed to fostering understanding of Eastern Christianity and reconciliation among Eastern Christians in a spirit of Christian charity. Good luck and welcome.
-- John