andrewdodd
If you have not been received into the Church yet, you can appraoch your Eastern Catholic priest and tell him your desire to join their Church. You are canonically not a member of any sui juris Church until you have received your baptism and confirmation.
Also, know that being a member of any other sui juris Church doesn’t prevent you from becoming a regular parishioner of any other sui juris Church. You can be canonically Latin and yet exclusively go to an Eastern Church of the Byzantine Rite. Although I imagine when it comes to marriage and Sacraments of Initiation, you may be asked to go to your Church of Patrimony (I hope I got the term right). You may apply for a Canonical transfer and I believe its easier for a Latin Catholic to become an Eastern Catholic than for an Eastern Catholic to become a Latin Catholic. I forgot which Pope, but a Pope forbade missionaries and anyone from converting Eastern Catholics into Latin Catholics. Since they are small in number by comparisson, the Church wants to do her best to preserve the people who preserve the traditions of the East.