November being peak season, would suggest you to do your bookings now as the hotels there are small and the good hotels get sold out pretty fast. For Andaman, I would recommend Megapode Resorts. This is run by the Andaman Tourism Authority and is a pretty decent resort. Take the sea facing cottages for the ultimate view and experience. There are only 4 or 5 of these so book them early to avoid disappointment.
For Havelock, you have to book a ferry. You have 2 options, the govt ferry or the Makruzz Catamaran. Makruzz is private, is more expensive than the govt ferry and runs only once a day from each port but is faster. I wouldn't recommend the sea plane as I've heard the schedule is very erratic and they have very expensive luggage norms (like Rs100/kg or something) but you're free to explore that option. The best resort there is Barefoot Resorts but it is expensive. It again has very small number of rooms so book early to avoid disappointment. If you want a cheaper option try looking at Eldorado Beach Resort. That being said Havelock has very basic amenities and infrastructure so don't expect much except nature.
Rest there are a lot of things to see and do so it really depends on how much time you have on hand and whats your budget. Do some research and if you have any questions drop me a PM. Tours are aplenty and you don't really need to worry about doing prior bookings. Even taxis can be hired once you land and its cheaper to do that rather than pre-book but have your hotel arrange a pickup at the airport for you.
On a personal note, if you're planning a trip to Andaman from North India, I would actually suggest against it and rather you visit South-east Asia instead. The infrastructure is better, the experience is better, its cleaner and the cost is roughly the same. In fact the amount you would pay for hotels in Andaman, you could get into some very good resorts in Thailand or Malaysia.