Hello Ragesh, last week we had trip of Goa with same question in our mind and believe me it was awesome experience and it doesn’t actually matter what the temperature is outside because, no matter what, you will feel relax when you are on the beach.
And if you are planning budget stays you can directly go and book hotels or home stay near the beach area and in this season it is really cheap we were 5 friends and we stayed at 1bhk bungalow 2000/day with two ac and refrigerator, you can find details of trip at my published trip Pune To Goa 4day 3 Nights.... https://www.tripoto.com/trip/goa-calling-5c7eb28b166e4?source=imessage hope that would be helpful.
Its a good and chill time ( in October) to be there before christmas.
You will enjoy much and have your own time there.
I recommend you to stay near Arpora , which has good connectivity to baga beach(famous) and nearby Saturday nightmarket and beaches.
Yes you can get homestays as well as apartments over there.
October is the beginning of season in Goa and in Airbnb you will get plenty of homestay options within every budget. You can also check prison or jungle by the hostel crowd, both are hostels but truly an amazing place to be if you are with a group of friends and would like to meet travellers from different parts of the world. They also conduct nice gatherings in the evening