If you go to goa
then you must visit aguada fort, ashwem beach and vagator beach, Chapel of St. Francis Xavier Basilica of Bom Jesus and obviously dont forget to taste konkan cusine of goa,
for stays if you stay near callangut beach
it will be easy to visit baga beach and candoli beach which are nearby and it will be a single road till the ashwem beach and vagator beach including anjuna beach also which can be a plus point to save time and in callangut beach you will get well maintained ac rooms at lower charges for night life and beach shaks baga beach is the best
Try water sporting and partying at any of the North Goa beaches which have an electrifying vibe in them while south Goa beaches are soothing and secluded beaches. Talking about the hotels go for any guest house near beach the cost will be roughly 3000-5000 per night, I'd highly recommend you to check oyo, they have good price listing. Search for an Oyo near some good beaches may be Baga Beach or Vagator Beach or Calangute Beach. Hope this helped!