mumbai to delhi to kathmandu

we are coming to mumbai to go to kathmandu .so we have to go to delhi to go to kathmandu .I was wondering should I take train or air .This is my first time to India.which class should I take if i take train where noone can come to our cabin.I heard sleeper class other people can be walking and I dont feel safe .I would want to have some clean and quiet area where vendors wont disturb my sleep.

How much it cost and From delhi to kathmandu how much it normally cost to fly.I know the train is gonna be so much hassle.what is the best way to go to kathmandu.I am us citizen and my wife is nepali she can speak indian language but still I want both of us safe.
both of us are new in India.any help will be appreciated.