We pretty much have the same requirements as Catholics… The bread must be unleavened, made of water and wheat flour with nothing else added. The wine must be red wine (my parish uses Christian Brothers ruby port, but that’s just our preference). I believe there was a council called before the schism between the East and West (I can’t remember which one), where it was decided that the bread had to be flour and water only, and that’s been the tradition in the Western Church ever ever since.
As far as the host itself, the priest uses a larger host for the altar, along with smaller hosts for the congregation, all of which get consecrated at the same time. The altar bread is broken in half at the Fracture, and a small particle of the piece the priest will consume is dropped into the chalice, with the words: “In token of Thy great descent into the limitations of matter, we rend this Thy holy body, that we may live, praying that by this action ordained from of old, Thy will, Thy love, and Thy consciousness, which Thou dost give us in this holy sacrifice, may be spread abroad upon Thy world: And as Thou, O Christ, art ever made known to Thy disciples in the breaking of bread, so may Thy many servants know themselves to be one with Thee, even as Thou art one with the Father.” The Deacon and Subdeacon receive pieces of the altar bread, as do any minor order clergy, if there is enough; and the smaller hosts are distributed to the congregation.
Because we’re more of an esoteric Church, the idea here is that in dropping the particle into the chalice, a connection is made between the elements of the Eucharist. When the priest drinks from the chalice, a connection is made between him and both elements, which is then continued through the congregation as each one of us receive the Eucharist. We also receive Communion by intinction, so the host is dipped into the wine before we receive it – but if, for whatever reason, someone prefers to receive only one species, they may. The fullness of Christ is contained in both species, so nothing is lost there.
I do agree that unleavened bread and wine would have been used at the Last Supper because it was Pesach, when leavened bread wouldn’t have been used. I believe, if I remember correctly, that the reason the Orthodox use leaved bread is to symbolize the resurrection. I could be wrong, but I think that’s a beautiful way to look at it, if it’s true!