Hey,
3 days for North and 2 days for South Goa seems good. You can also probably visit Panjim and Fountainhas if you have time.
For stay and places to visit check out this link - https://www.tripoto.com/goa
Hope this helps.
You can stay at the cottages on the beaches, that are more budget friendly especially at palolem/patnem beach South Goa. Also for chilling out, go to cola beach and galgibagh beaches they are more peaceful and calm