I'm an advocate of merging the air force, at least in Southern India, into the navy; aircraft carriers would help India project its military forces over a wider area, including fighting on the European side of the Middle East, the Arabian Sea, and the South China Sea.
I think India should focus on transferring/replacing most existing aircraft in the South to the Navy, and that the Navy should be provided with supercarriers to act as "moveable bases", as this would provide India with more flexibility.
I would choose the HAL LCH and HAL FGFA for any new procurement. I highly doubt that any conflict in the South would be fought on land, and the conflict that I can imagine happening can be easily fought by paramilitary/gendamerie.
My only concern with the HAL LCH is that it's somewhat weak and wasn't built for the purposes that South India would need to defend from. SK's navy has procured the AgustaWestland AW159 Wildcat which is markedly more powerful than the LCH, and it's also built around the concept of naval warfare and anti-submarine operations.
North India has very little use for a navy. It should build a wall and focus on counter-terror operations (paramilitary), with a sizable air force and land force for skirmishes along the border.