Delhi will be chilly in Feb - maybe 10-15 degrees or so.
Mumbai & Goa will be around 30.
So take the necessary clothing, although you could travel light and buy cheap when over there and give what you dont want to carry to a beggar - they will get a few rupees for it.
If you are a beach person, you probably wont want to stick around in Mumbai or Delhi too long, as they are pretty busy places. If you are a city person, the nightlife in both are great. Mumbai especially - lots of Bollywood stars will be out in the clubs, but booze is not cheap in those places.
Accomodation ranges from €30 per night (this will be very basic) with no upper limit in the cities, possible cheaper if you rough it and stay in a dorm in the less touristy areas.
In Goa, you could get a basic shack for €10, again with no upper limit - you could pay hundreds in the 5* hotels, but saying that, they do have deals for say 2 / 3 nights.
Really depends on what you are after and what your budget is.
Train Mumbai > Goa is about €20 each way (12 hours), but it is only one hours flight and you could get that for the same price.
Look at Air Deccan, SpiceJet, Go Air, Kingfisher Airlines - They are some of the budget airlines. There are 5:30am flights - usually cheap and you could be having breakfast on the beach by 7:30.
A GREAT forum is
www.indiamike.com - Definitely check it out and bring a good book - Lonely Planet, Rough Guide etc.