To get "survey grade" GPS results, you need corrections. A single unit, such as what you buy at Walmart, or the unit in a phone, is accurate to a few feet. In the horizontal direction, this is probably good enough, but for grading, a few feet of accuracy isn't very good in the vertical direction. You can pay for base corrections, some ag companies offer it, but its still the same thing, the elevations probably aren't good enough. Some states offer corrections, some are free, some aren't, and some survey suppliers offer it. Trimble offers it for the state of Illinois, but its pricey, a few thousand dollars every year for a subscription.
An alternate method, and the one I use, is to have a second GPS reciever. The GPS base sends corrections to the rover with a radio, or a cell phone link, and you have accuracy of about a 1/4". This also requires a clear overhead, ie no trees or very few trees. A typical machine control is two antennas on each side of the blade, be it a dozier or motor graders, a reciever, and electorics the operator can view. This is usually also tied into the hydraulics of the machine and when the operator gets the grades close, the machine does it for the operator. This type of set up is very pricey. This can also be done with a rotary laser, but you don't have any horizontal control, but depending on the project, it might not matter.
Another problem with machine control is you need a "grading file". This is basically a 3D model that tells the machine how to grade the project. For large highway jobs, this 3D model can cost tens of thousands of dollars. In the long run, this saves a lot of money, you don't need as many stakes, the operator is more efficent, and the job goes quicker, but the intial investment is pricey and probably beyond what you need.