You still have time to apply...

I was exactly same as your situation (green card, living in US) when I applied visa to Italy back in 2006. If there is one consulate office in the city you live, you can go up there to apply and get it withine one day. If not, enclose a letter and let them know your trip date. They will consider it and get back to you on time. Enclose a pre-paid Fedex return envelope. You don't need to buy tickets in advance but it will help if you have an itinerary with your flight date and hotel reservation (but not necessary).

Good luck.