Villa 'Duas Palmeiras' in Fatona. I think it's around 90-110 euros per night. You can google the name and you will find several platforms where to book. A friend went sometimes back and recommends it.
Hello, October is a great time to visit Goa as there will be less crowd and prices will also be less (on stay, food and activities) as compared to months December and January. You can choose some great stay options as per your interest and budget here: https://www.tripoto.com/hotels. Villa is best option for group stays and you can find them in areas such as Palolem, Varca, Fatrade, Loutolim and Vasco da Gama to name a few. Happy travelling!