Don't be too quick to hire or buy a dozer, check into an excavator first. Won't tear up the ground as much and in my experience in the woods here an excavator is cheaper and faster. Excavator can do a better job of piling, too.
You really need both, however it can get expensive fast. My rental agency charges $120 per hour to move the equipment back and forth, so being an hour away from the shop, it would be $500 just moving (2) pieces of equipment to and fro to my place.
With an excavator you can dig and pile, but are unable to move the stumps any appreciable amount of distance. Its not such a big deal if a person can burn the stumps, but a big problem if a person is pushing them to the edge of the field. Burning is the better option, however it is also means a lot of liability...stumps burn forever, and if a couple shooting off a bottle rocket for a gender-reveal party for their baby can start a California wildfire, imagine thousands of stumps burning for a year or more? It is kind of scary to think about, not to mention a year of your home smelling like smoke, neighbor complaints, etc...
Forget about burying stumps though because it takes too long, requires deep soil, and when they rot down eventually, it will leave a rough surface full of holes that can snap the legs of livestock.
That is why I mentioned the bulldozer. With one piece of equipment a person can remove stumps, push them long distances, and grade the area when done. It means only renting and paying to move one piece of equipment.
You can also dig somewhat with a bulldozer. For instance, a person can cut a slot with a bulldozer and bury rocks that way. This is the trick I use for getting rid of rock walls, which is incredibly trying for a person clearing land. I just get on one side of the rock wall, cut a slot, then push the rock wall into the slot, and regrade with the loam removed to make the slot. It takes time, but saves pushing the rock wall to the edge of the field...
But if a person has unlimited money, the best option is to take an excavator first, remove the stumps from the ground, then let the stump sit over the winter. The frost will knock the dirt off the root ball so when you come back the following summer with a bulldozer, and push the stump to the end of the field, the dirt has fallen off.