In the pioneer days, one of the tools all the farmers hauled with them from back east was a mule drawn bottom plow and axe and shovel. You really cant farm with only one tool although many additional tools can be made from local wood when you have axe and hammer.
Now if you are talking more modern day (after mule power) small farming with a tractor, I would guess that a disk would be a necessity for breaking up the soil. One could plant by hand, weed by hand and harvest by hand if needed. It would be much harder to turn the soil by hand or with spade with any acreage at all. But in truth, minimum implements to go with your tractor would be a disk, planter and cultivator for farming. Multiple hand tools are required to keep them operating, like a forge, hammer and anvil for sharpening plow points and fusing metal together (no welding machine after civilizations has collapsed like in SyFy movies) but then you wouldn't have any fuel for your tractor either so better keep those mules/horses/oxen around unless you have a strong back to pull that plow.
When you get to really thinking about it, you really cant do a lot with just one tool or implement unless you go big with the specialty equipment like 40 row implement draw by 300 HP tractors that break the ground and form the rows, plant fertilize and spray herbicide in one pass.