It depends on time which you are going, I was there in december for 25 days, stayed at palolem. if you are planning this months stays are cheaper you can take beach huts as well Or hardly 5 mins walking distance from beach crystal goa is also there if you want to stay at proper hotel kind of place. in beach huts you can check cozy nook Or dream catcher they are amazing.
For 3 days and in February you can easily get a good beach facing shack. with a budget of 10k for 3 days Go for Art Cafe or Ourem place. Or you can also check, Cozy nook or Dream cather. Go for AC shacks only at a place where you can have good food as well. Note- Prices will be highly negotiable at that period.