I wrote a few posts in my blog about learning some Greek.
Since the most important thing is to know what each letter represents, you might not need a memory palace. You could probably get away with just creating a link between each symbol and its sound. The memory palace would only come in handy if you want to memorize them in order from the beginning. (I never learned the exact order of the letters, but only learned to read words.)
I don’t know much about Ancient Greek, but here are some quick examples with Modern Greek sounds:
These are the same as in English:
Α, Ι, Κ, Μ, Ν, Ο, Τ, Ε, Ζ, α, ι, κ, ο, τ
These are similar to English – just remember the shape or sound variation:
Β, Δ, Υ, Ω, β, γ, δ, ε, μ, ς, υ, ω
These could be linked to mnemonic images:
Γ — picture a guillotine – it represents a “g” sound (or cross between a g and y)
Η — picture a waterslide and the word “wheeeee”
Θ, θ — picture a thorn stuck in your fingertip (“th”)
Λ, λ — someone turned the L on its side and flipped it over
Ξ — an arrow was shot through an X, splitting it
ξ — the pieces of the X then fly away like balloons with the air let out of them
Π, π — pi
Ρ, ρ — tennis racquet (“r”)
Σ — someone twisted the bottom of the “S” around
Φ — fava bean, ready to split in two (“F”)
Χ, χ — imagine clearing your throat to spit on an “X” target
Ψ, ψ — Poseidon’s trident (“ps”)
ζ — something like a cursive z
η — an eeee-ear (“i”)
ν — pointing dowN (“n”)
σ — rolling Stone (“s”)
φ — a face (“f”)