As this is your first time and you would like to explore the famous places.. stay near calangute and baga beach... acerage budget place i would suggest is bloom suites.. hire a 2 wheeler.. you will get someone through hotel.. sit on beach side shacks.. order food and drinks n chill.. you can then hop from one beach to another.. chapora fort before 5 pm.. vagator beach for great sunset.. There is a tito lane with famous eateries.. chill and enjoy
You should go via road.
places to visit
Aguoda fort dolfins near agauda fort
reis mogos fort calangute beach miramar beach baga beach titos lane vagator beach anjuna beach arambol beach
north goa for fun and south goa for inner peace
See, if you are a party person than stay in North Goa and must visit calangute and baga beach. You may note that North Goa is very crowded and you fill find n number of footfall on these beaches. However, if you are peace lover than you can stay in South Goa and visit many famous beaches like Colva bech, palolem beach, Agonda beach, Bogmalo beach, etc. Mostly all the beaches of South Goa are silent and cleaner than North Goa. However, if you are looking for the combination of both party and peace than you can stay either on calangute or baga and then can also visit Ashwem beach which is clean and silent beach in North Goa. You will find very less Indian crowd there as mostly Russians and other foreigners prefer this beach because of less crowd and silence. Let me know if you want to know anything else. Regards,
From Mumbai you get direct buses or flight to Goa. Buses will drop you at Panaji, capital of Goa. From there you can go to Anjuna beach (North Goa). Anjuna is good as this place is good for party and live crowd. If you want to get away from crowd and look for some peace then you can travel to South goa beaches like Palolem, agonda beach etc.