One of the things I've noticed in becoming familiar with various traditions in "apostolic Christianity" is how daily prayers get more "liturgical" the farther East you go. RC prayer books have some liturgical prayers in them, maybe the order of Mass, etc., but the bulk of the contents are "devotional" prayers, novenas, etc. I own four EO prayer books, two of the "Greek" tradition and two of the "Russian". They have more liturgical prayers, but also seem to contain what I'd call "devotional" prayers (unless these prayers are liturgical and I just don't know where they could be found). All of the OO prayer books I've ever seen contain only liturgical prayers. So, while you could start your day as an RC with a Consecration to the Sacred Heart and various prayers to saints and for various needs, or as an EO with basic prayers, troparia, Psalms, and other prayers, liturgical and not so liturgical, if you start your day as an OO, you will be directed to the morning services of the Church, period. If the people choose not to use those, then they invariably figure out something for themselves, usually private prayer and Scripture reading for example.
Our tradition is to pray without shoes. In church it is mandatory, at home people usually have their shoes off anyway, but if you do have your shoes on for some reason, you take them off. This does not apply, of course, to certain situations like praying before meals (I imagine it would look strange to onlookers to see a person take off their shoes at McDonald's for thirty seconds while saying grace). I always wash my hands before prayer, but there is no specific ritual or prayer for that. I don't even think it is "mandatory". I do it, and I can't imagine it any other way. I don't know what else there is to say, I would think it is very similar to other OO/EO practices.