DEL in Jan also means Fog - so flights do often get delayed. Ideally avoid DEL and instead do BOM connecting to the morning 9W 479 (6:30 AM I think) flight. BOM-GOI is a 1 hour flight - so you can take Business class but you really wont have time to enjoy it.
Alternately do LHR-BLR and connect to 9W or IT. Again a 1 hour flight.

GOA in Jan will be very crowded so do your bookings now. Leela is ok, Taj exotica is nice as is the Park Hyatt. All have (largely) their own beaches and you can always hire a car and drive to the louder and buzzier beaches if you like (but Leela is way down south whereas all the "fun" beaches are up north)