I've started learning Ancient Greek and have bought Athenaze Book 1.
This is my approach to Ancient Greek phonology.
Epsilon, eh psiilon
Zeta (zdeta or maybe zeta for Koine),
iota, (i or y)
xi - ksii,
upsilon (french u)
xi (German ch- chii)
omega (o extended)
I don't feel comfortable with the aspirated k,t,p so I wouldn't talk like that.