There are loads of places to rent, especially in February, I suggest that for the first night you book into an hotel then the following day, look around for an apartment, any of the tuk tuk drivers, will tell you where there are apartments, and all you have to do is wander around in the area you wish to stay in, and there are always notices saying apartment, villas to rent.

Look here - http://www.ownersdirect.co.uk/India-Goa-2bed.htm

I can highly recommend this one http://www.ownersdirect.co.uk/india/IN36.htm my daughter stayed here in February.
It is brand new and in a quiet location behind Victor Exotica, Candolim.

You can get better prices locally... There are apartments to rent for around £100 a month (as long as you're not coming in Dec/Jan)... I would say you could get something for at most £150 per month if you spend a few hours looking/asking..... - get the price before you look to save time. Say you've got a budget which you have to stick too.. Most places are designed for 3 maybe 4 people to sleep (2 bed apartments), should come with stove and fridge as default.

for your replies, will have a look around when I go in November.