Every project runs short of money. All of them. Surprises surprise, changes are made and prices for various components go up. The best way to ensure that costs spiral out of control is to go in with a vague wish list and hope for the best.
The best way to minimize overruns is to clearly define your project and give your contractor the opportunity to steer you away from decisions that will blow the budget.
Good contractors are a great resource for cost saving tips. They know what is easy and hard for their crew and they are well versed in local construction standards. While you are getting bids from contractors, ask them “what can we change to save money without changing the overall quality of this design?”
It is a good idea to tour projects completed by your contractor. Ask him or her for examples of their cost saving ideas to ensure that their taste and quality standards match yours.