My choice would surely be Lalchand Rajput. While so much is said about Gary Kirsten's role, the short-lived tenure under Rajput has had a lot of success. He's good with the younger players, and being a former Indian player, he'll interact well with the seniors. It's anybody's guess what he's done to win titles with nearly every team he coaches, but he was never given a real chance. Of all the Indian coaches to choose, he's surely the best. Let's give our own elders a chance; they're now qualified and have experience.
Ideally, the next India coach should be an innovator. He should introduce something novel into the team, that makes it better. Rajput never got to innovate much, though results were good. Kirsten was hardly one who introduced anything new, likewise Wright, and it was just the players being good or getting better that helped. Chappell was a serious innovator and took huge steps, but a whole lot of wrong decisions were taken. It also didn't help that he was very, very grumpy. There is scope for innovation in this team, and it should be explored. Player retention and sustainability is also a factor. A lot of players were lost or cast aside under Wright, Chappell and Kirsten, and many could have made a difference to the Indian side. Moreover, the India coach should follow the domestic scene or at least have his deputy there, to brief him. Lastly, coaching India is a high-pressure job. Can the man take it? That's also a factor.
Stephen Fleming isn't such a bad option either, but a lot of CSK's success has been with overseas players, and only lately with a few more Indian hands (Vijay, Ashwin). Besides, would you have a T20 specialist coach as a full-time, cross-format national coach? It's a long shot.
Dav Whatmore is another option to explore, but the Lankans' WC96 win was long, long ago. He's had decent success with Bangladesh, but sources indicate he was another Chappell, of a lesser degree.
Let's leave Warne out of this. He doesn't seem too interested. He's a limelight-hog, much like that other celebrity Australian coach. He doesn't seem too innovative, and is very much a preacher, and relies on faith instead of method.