1) It is not mentioned in your querry that where is the Immovable Property situated.
Probate proceedings shall be applicable for notified Cities. If the Property situated in those Cities you have to apply to the Court for grant of probate of Will.
2) If the Property is situated in the area which is not covered under Probate proceedings, you can file a suit for Declaration of Title and Possession (in case possession of the property is not with you) or Suit for Declaration of Title and injunction ((in case possession of the property is with you) if you have any threats from your aunts that the possession of property is being lost.
3) when you do not have such threat, you can simply go ahead with the Will executed by your Grand Mother. Basing on the Will you can apply for mutation and you can also start construction.
But there is every possibility of filing suit by your Aunts for partition of property, ignoring the Will, as your grand mother died intestate. in such a case you have to contest the case and prove the execution of the Will by your Grand Mother in your favour.
The Burden of proof lies upon the party who propounds the Will to remove all the suspicious circumstances surrounding the execution of will to the satisfaction of the Court.
You pls check the following:
1) Whether the Will was registered? of course there is no difference in the eye of law between registered and unregistered will. Still you will be in better position and can avoid plea of forgery.
2) Whether your grand mother had revoked the earlier will by mentioning relevant words in the Will executed in your favour. (it is relevant to prove her state of mind at the time of execution of will).
3) Who are the attestors of the Will? are they interested in you? if the attestor is your father or mother etc. you have to take much pain in proff of the Will.
(the attestors will play crucial role in proof of execution of will saying that the executamt had executed the will with her free will and in sound state of mind)
Proof of will itself is a big chapter, it is difficult for me to list the probable querries you will face in proving of your Will. You may consult a good civil lawyer in your area and take appropriate decision.