The version I learned at school, which we were made to sing while learning the steps:
Άιντε Καραγκούνα, Καραγκούνα, άιντε σε σι πρέπουν τα σιγκούνια
Standard modern Greek: Καραγκούνα, εσένα σου πρέπουν τα σεγκούνια = σου αξίζει να φοράς σεγκούνια
English: Karagouna, you deserve to wear a decorative overcoat
According to Greek Wikipedia, only married Karagounes wore the full outfit, which included the said sleeveless ovecoat, young women wore plain dress, so perhaps the meaning of the verse is that she deserves to get married.
Here is an image of a decorative sleeveless overcoat (σεγκούνι), although it can also be with sleeves and comes in various colours- however the Karagounes usually wore black
Αμ πώς δα, αμ τί δα, στο παραθύρι σ'είδα
Αμ πώς δα, αμ τί δα, την προκοπή σ' την είδα
Αμ πώς δα, αμ τί δα both mean roughly "what did you think?" as in did you think he would make up his mind (that she is a suitable wife) without doing his research first? στο παραθύρι σ'είδα/ την προκοπή σ' την είδα I saw you at the window/ I noticed your industriousness.
θα πουλήσω και τα γίδια
να σου πάρω δαχτυλίδια= I will sell the goats and buy you rings
θα πουλήσω και τη στάνη
να σου πάρω ένα φουστάνι= I will sell the sheepfold to buy you a dress
In other versions the Karagouna does not deserve a segouni (δεν σι πρέπουν τα σεγκούνια)- implying she deserves to wear western style clothes, and her suitor instead of noticing how hard working she is, tricks her into giving in σι γέλασα, σε πήρα.
Notice the pronunciation of central Greece where ε is ι, as in σι= σε, not to be confused with συ= εσύ
Perhaps the title of the thread should change to Καραγκούνηδες (of all kinds).