How deep to dig depends on how deep the unwanted plant roots go. Some, Dandelions, can have roots that go down 12 inches with no problem while others, Chickweed, will only be just below the surface.

Yes, you "will probably need someone to keep on top of the weeds" forever. Just as other gardeners do.

No one gets a free ride in a garden or landscape!

Make that weekly. Weeding is a regular job in gardening and little and often is far more effective than waiting for a jungle and then doing a huge splurge.

As the digging, it needs to be as deep as the weed roots, as kimmq said. A fork or spade's depth is a good start and that is more than 6 inches. A garden fork is a good tool for weed digging as you can roughly sift the earth as you turn it using the tines.