I think for goa u should plan on ur own as in goa u will find a hell lot of hotels and hostels to stay in !!!and then u can rent a two wheeler to roam around!
Big No to packages! Goa is a place where lot of college students come on budget; so does not make sense to pay a premium in a package. Also, you could see most of Goa on a two- wheeler; the only thing you would need is google maps:). I would recommend Jan-Feb or Oct-Nov as the time period as Dec prices are generally high. In your first visit, try to stay in North Goa as the beaches there are much closer to each other and the shacks/night life is more upbeat compared to secluded and laid back South Goa beaches.
Obviously you should plan your trip on your own. You will save a lot of money by planning your trip yourself. You can get cheap accommodation at Zostel/Backpackers Panda.
For how many days are you planning your stay in Goa.
Instead of booking an entire package you can book only sightseeing for 2 days (North and South Goa each day). You can get in touch with any hotel as it charges nothing more than Rs. 250/- to Rs. 400/- pp each day. The remaining days you can spend hiring a moped or car which is easily rentable at every corner. And view as per your wish.
North Goa is highly recommended.
I would just tell you keep it unplanned Go by railway Take bikes from hotel And wander like hell Explore as much as you can because if you go on planned or package trip you will be time bounded