Would starting up a construction company in India be a wise thing to do? What part of India would be the best to do it?

Unless you are of Indian decent I would forget it. There is a lot of red tape and as a FN your are not allowed to buy land or property. Not only that but it is difficult to get reliable labour. My wifes(NRI) nephew has his own construction business in Surat and even he has trouble keeping labour and he speaks the language.