We have a list of recommended relocation companies in India which might be worth checking out. Our section on Shipping and Removals in Mumbai gives an overview of what to expect throughout the relocation process.
I think you have to right idea about not taking furniture with you – you'll be able to save a lot of money that way. Regarding insurance, it's generally a good idea to insure the goods being shipped with a company separate from the company doing the actual shipping.
Best of luck with the move!