What will be the best location to stay?

Hi all
I hope my post is still alive!!

Your post is alive, all right. 
You have mentioned pretty much 4 out of the 7 Emirates in UAE, so it is not possible for anybody to suggest a place to stay.  Each place you listed is its own city, with its own plus and minus.  Sharing accommodation is possible in each place.  Suggest first you finalize your location and come back with this question.
That said, between Shj, Ajman and Dubai one could stay in any location and manage the other two if you have transport.  Ajman would be cheapest and Dubai the costliest.  For Abudhabi, you will be better off to stay there itself.  There are people commuting from Dubai, but doing 300+ km each day will drive you nuts.
Sharing transport is possible, there are risks associated with private ones.  Public buses and taxis are available between the cities listed.
Food is not too expensive, and it is only as costly as you want to eat.  There are thousands here who manage within AED 500 a month, and equal number who spend 10 times that.  Self catering always is the best moneywise and healthwise.  The restaurants in UAE have a minimum quality standard, so it is not too bad.
The phone companies (Etisalat and Du) have some offers to call India, you can use them.  Internet calls are there too.  This is not a major problem anymore.
If you came back with more information like your estimated salary package, location etc, this forum can provide more input for you.

Live on the place nearest to ur work.food no problem its cheap.bedspace all available or room   dubai is nice just embrace it just be optimistic.