The best way is to hire a bike... if this is your first trip to Goa you can also book the Hop on hop off bus tour which costs Rs 400 per person for 1 day tour and Rs 700 for 2 day tour... This tour covers the major attractions of Goa and is a fun way of sightseeing...
You can rent a two wheeler if you plan to stay in North Goa or south Goa alone! However, if you are planning a trip from North to south Goa or vice versa you can rent a 4 wheeler as well. If you don't want to drive, you can hire drivers too.
I visited goa recently the best way is via scooter starts from 350 make sure you rent a scooter with yellow plate or else you will have to pay fine for same. If your driving skills are good then you can also plan visit to dhudhsagar which is almost 80km from mapsa city.
If you are a group of 2-3 people then the best way to roam around goa is by renting a bike in around 200-400Rs per bike per day depending on the season. But if you are around 6-7 people then try renting a Thar. It would cost you around 1200-1400Rs and would be complete different experience.
If you're a small group of 2 or 3 people, it'll be more economical to hire a 2 wheeler which is very easily available throughout North goa. If you're going in a larger group and want to explore more of the state, I'd advise hiring a car.
Also, be wary of the month you are visiting goa. During the peak seasons, bikes can cost up to 1000 rs per day.