Hi

I'm not sure about Athens but I am moving to Thessaloniki and have worked out the following:

Rent approx 500 Euros (possibly furnished)
Car: 1-2000 Euros (second hand)
Utility bills 150 (approx per month)
Food/shopping 600 (approx home cooking etc )

you will need to earn at least 1200 euros per month, as for the school if you are going to pay for private english school that will be expensive....for a rough estimate look up Pinewood school Greece they have some prices. If you are in a well paid job you should be ok. Unfortunately Greek wages are not much thats why I will be working in UK during the winter..

Good Luck!