Bus - The state-run Kadamba bus company is the main operator, although there are also many private companies. Local buses are cheap services are frequent and they run to just about everywhere. Destination signs at the bus stands are in English, so there are no worries about finding the bus you want. They are, however, fairly slow because they make frequent stops.
Car Rental - Self-drive car rental is available in Goa, although it's expensive. Several companies have counters at the airport. It's often cheaper, however, to rent a taxi for a specific trip.
Motorcycle Rental - Hiring a motorcycle in Goa is easy, and popular with many travellers. The machines that are available are Enfields bullets, Yamaha and plently of many modern Bikes.Prices change according to the season. Some places need your passport and a sizeable deposit before they'll let you go; others just want to know where you're staying.
Motorcycle Taxi - Goa is the one place in India where motorcycles are a licensed fotm of taxi. They are much cheaper than other transport, and backpacks are no problem. Licensed motorcycles are common and can be identified by a yellow front mudguard.
Bicycle Rental - There are plenty of places to hire bicycles in all the major towns and beach resorts and this a great way to see goa if plan to stay in a particular area for some time.
Boat - One of the joys of travelling around Goa is the combined passenger/vehicle ferries that cross the small state's many rivers.There are plently of private boat operaters who u can arrange for cruise etc .
P.S You should be aware that India has the worst record for road accidents in the world. Please observe all traffic rules.