Divide the state into two - North Goa and South Goa as there are many attractions to be covered in both the parts. You can spend the first one and a half to two days visiting those attractions and you can spend the last day relaxing by the beach or indulging in adventurous sports. Bungee Jumping has recently been introduced in Goa but I don't know if it's operational during these times.
There are two type of trips, when you plan for Goa.
First type- Party, loud music, don't care and have fun, and famous and crowded places exploring.
For this type, you must go to North Goa, preferably calangute and baga beach. (Highly recommended if you are the first timer to Goa).
Other North Goa beaches Like Anjuna and Vagator are even better for this. Arambol is little different and is a very beautiful beach to be. must go if you are visiting north. Second Type- Calm, chill, explore the real Goa and live and not so loud music. For this you must go to South Goa, Palolem beach or Agonda. All other beaches in south dont have anything after 10 PM. stay and enjoy near these, explore other beaches or places during the day. You can do water sports both in North and South. Decide, which type of trip you prefer and have fun!!