I travel all the time and am ex cabin crew, and my little one is a seasoned traveller at only 9 months . It's not as hard as you think....
The best seats for you would probably be ABC or HJK seats as you have booked 3 seats. This means no one climbing over you and just your family in the space. Check on SeatGuru for exact seating plans although they do not mark out the bassinet seats so check on airline site.
Bassinet wise British Airways have facilities for a special bassinet for up to 2 years old, which is perfect for a 1 year old and you can choose you seat online at point of booking if travelling with an infant.They let you carry in the hold your pram and carseat.You will transfer from LHR/LGW. There are no strollers available for use whilst in transit.
Qatar airlines offer a free sky nanny service so you can rest a bit even in economy, whilst you watch a movie or sleep. You'll transfer in Doha and have free strollers to use whilst in transit. They also let you take your pram and carseat.
Emirates airline provide a baby ammenity pack with a rattle, wipes, talc etc and have spare nappies and food on board. Great inflight entertainment (ICE) on demand system. you'll transfer in Dubai but they have free strollers for you to use at airport.They also let you take your pram and carseat into the hold.
Virgin Atlantic only let you take your pram OR carseat in the hold.So you will need to hire one at your destination.
New Delhi has free strollers available for use in Terminal 1D of Indira Gandhi International Airport.
Please see my other tips on www.flyingwithababy.com which will help make your flight easier.