The GPS process you are looking at is termed Real Time Kinematic (RTK) GPS. The stated specification in the horizontal is generally in the 5mm (0.017’) range and 15mm (0.05’) range vertically. Please realize that the specifications are only a single part of the error budget, there are several others such as rod measure ups, length of baseline, multi-path and so on.
One Man total station surveying is performed with a Robotic Total Station.
As a rule of thumb, RTK will get you about 0.1’ of accuracy if (big if) there are no obstructions. Trees are a very common source of error and even if you get a lock under the trees, then you must contend with multi-path errors. Multi-path is when the radio signal is received directly by the GPS unit and also a secondary signal which bounces off of other objects. RTK next to buildings and fences are also big issues here.
The length of the baseline further degrades the value of the solution. With VRS you generally have very long baselines.
The vertical element of RTK is the weakest.
Robots are generally very precise and while they do have a line of sight limitation, there are no issues like tree canopies or shot placement next to buildings to contend with.
Depending on the budget, the first equipment to purchase would be a Robot, the second RTK GPS. At least that is how I did it. I am a consulting Land Surveyor and have quite a bit of time doing One Man applications.