"I go and play."
Translation:Εγώ πηγαίνω και παίζω.
First, I am surprised you "normally don't have any problem with latin transliteration" because the course does not allow transliteration any more supposedly... (https://www.duolingo.com/comment/23350148)
Second, you would have to look at the transliteration rules that were used when transliteration was allowed: https://www.duolingo.com/comment/17556409
And third, it would have to be paizo or pezo, because it's a Z sound and neither of your options reflects that. :) Of course, you would have to try it with all other combinations for πηγαίνω...