Since it is the Ethiopian Church that you wish to join, I would think that they would baptise you. There are, as stated above, exceptions. From my experience with the Copts (Egyptian) and the SCOBA Churches here in the US, I have seen plenty of intercommunion, particularly when there is no Coptic Church. I have found the Copts somewhat more hesitant to commune EOs, but I have personally seen it done, and have done so myself. I have found the issue of communion between the EO and OO to be somewhat of a "don't ask, don't tell" affair since officially we are not in communion. But I can tell you that in the Serbian Church that I attend, Copts and Ethiopian Tewahedo members are very highly regarded and loved by the Priest and many members. I don't know if this extends to communion since I have not seen this myself. However, the local Antiochian Church did commune Copts quite regularly before they built their own temple.
To directly answer your question, I would attend the Greek Church if at all possible. The RC would probably commune you, but I would not suggest you go that route. I will not go into my reasoning any more than to say that this is an ORTHODOX forum, and if I thought that communing with the RC was OK, I would be Roman Catholic myself.