Note: This may look weird, but that's because it's a Romanization, not a strict transliteration. Following this practice is why we have dinosaurs and not *deinosaurs (δεινός), music not *mousic (μουσική), and archaeology and not *archaiology (ἀρχαῖος).
Length is distinctive in consonants, thus /sː (s:)/
Gamma is /ŋ/ before /m/ (and /n/, too, I think).
The clusters represented by ψ, ξ were originally (where those letters had not been introduced) spelt ΦΣ, ΧΣ, implying that they were [pʰs kʰs]; for simplicity's sake and common practice it will probably be better to write /ps ks/ as the aspiration appears to be secondary.
Use /zd/ for ζ. Like it or not, that's the generally proclaimed value.
The digraphs ει and ου were originally diphthongs ("genuine diphthongs"). The diphthong ει soon became /eː/, opposed to the plain letter η /ɛː/. ου was originally /oː/ opposed to ω /ɔː/, but soon became /uː/. After the genuine diphthongs monophthongized, their spellings began to be used for their homophones, sounds previously spelled ε and ο (long, but like the other vowels α ι υ, not marked as such). Thus the "spurious diphthongs".
During this period iota subscript was still pronounced, though perhaps in the process of being lost. Thus, /aːj/, /ɛːj/, /ɔːj/, or perhaps like /ɔː(j)/.
The Koine greatly simplified the sound system of Greek.... Besides the obliteration of nearly all diphthongs, the pitch accent was replaced by a stress accent, ordinary /ˈ/. If there was a secondary accent I don't know how it would be placed...