The nine orders of angels are more readily available with the expansion of the web in the last few years. Being able to chant off their ranks seems to me a gracious antiquitarian knowledge.
SERAPHIM
CHERUBIM
THRONES
DOMINATIONS (or dominions)
VIRTUES
POWERS
PRINCIPALITIES
ARCHANGELS
ANGELS
The most euphoric summary of them is at this excellent page .
My particular favorite from the orders of angels is the Thrones. They are described as being giant wheels of fire. This, even before I learned:
1) through them the justice of God is pre-eminently manifesed; ... helping kings and masters to bring forth right judgement. here
2) Thrones reside at the point where the heaven meets the earth. beware the soundtrack
3) Ofaniel, their head, is the angel of the wheels of the moon, the wheels of heaven
4) they are many-eyed, like argus. ezekiel daniel