A number of patriarchs (there was five originally) which are bishops of specific churches. So the Bishop of Constantinople is actually called the Patriarch of Constantinople. Of those, the Patriarch of Constantinople is primus inter pares. His role isn't the same as Pope though Western Churches often interpret it as such. Think more of the Speaker of the House. He presides at meetings and settles disputes between other patriarchs.
Below that are the regular bishops. Some churches accept Archbishops, some not, I'll gloss over that. Basically an Archbishop is a super-bishop - of an important town say (though not important enough to merit a patriarch) or an entire region. It's important to remember, particularly at the time period you're talking about, the sheer amount of autonomy a Bishop could have. When messages from Constantinople could conceivably take months of dangerous travel, the Bishop was the man on the ground and wielded a large amount of power in the day to day interactions with his bishopric. There are a colossal amount of variations on the bishop theme, it's very much the base unit of Church administration. As well as archbishops above, the other major group are what the Western Church call Titular Bishops. These are bishops without a diocese responsible for...concepts. Phrasing this badly but say the Bishop of, I dunno, Antioch is responsible for the church in Antioch. However, the Treasurer for the Church might well hold the rank of Bishop as well, and his responsibility is to the finances of the church rather than a geographic area. Make sense?
The come the priests split in to monastic and non-monastic. On the monastic side, archimandrites oversee either a large abbey or a number of abbeys and are the only priests eligible to be Bishops (only ones who are priests, obvi). Below them, monks and hieromonks - hieromonks are also priests, monks aren't. On the non monastic side, Archpriest then priest.
Finally the deacons, who are laity. Archdeacon and deacon on the non-monastic side, hierodeacon on the monastic.
Shout if you need more. My Latin is pretty decent so shout up if you need anything or that as well. Greek is weak and in all honesty not much better than Google Translate