Dear T-bone, I would first recommend reading the Light for Life series for a basic catechesis. It is completely legit to attend eastern Catholic churches to fulfill obligations but I would caution you to something. If you find that you are interested in celebrating the Catholic faith through the eastern rite tradition as opposed to the western tradition, it would not be advised to jump from eastern to western often. I say this because we have different feast days and different nuances about the faith even though we are in full communion with each other. If you have children or are planning on having children then they are automatically the rite of the father so if you find yourself wanting to become a permanent fixture in an eastern church I would recommend changing your rite. This however should only be done after consistently attending an eastern rite for a couple of years. Our traditions are beautiful and retain so much meaning. I was once a Roman rite many years ago and was improperly catechized. I had no clue what was going on in Mass. Through my experience of the Divine Liturgy, I now have come to appreciate Mass more and understand what they are trying to do even though it is so "sterile."