First problem: Can you put some barrier along the road?, Field? to keep the equipment out of your Yard?

At 20' x 50' area is really not that large. I have problem keeping my wife's flower beds that small.

If it was me we would put in a flower garden, There are many types, Since it is now yard a woodland garden would be in the distant future. However my wife's most successful garden is planted to attract butterflies. This garden attracts all sorts of butterflies, and bird.

The hard structure consists of bird baths and bird feeders. Plants include butterfly bushes, lantana, and several other plants with flowers to attract the butterflies and birds. It also has seasonal plants like daffodils, and several types of bulbs. Forsythia is a beautiful spring bloomer. dwarf lilacs would also be a possibility of summer flowers. You may have to do some research to determine what is best in your area.

As for paths even though the garden would be narrow, paths are essential. First that invite people into the garden, and the also provide a paths to maintain the garden. I use stepping stones as some time plant growth is unpredictable, and the paths have to be rerouted around growing plants.

Once you get everything growing you will be surprised at what the garden will attract. We have had every thing from Chickadees to Vultures at our bird bath. Blue bird come for the insects, and other birds for the seeds. Occasionally we have had some beautiful hawks in our garden.

We put markers at the edges of our driveway. They are for sale in every hardware store in the fall. When we had a plowing service, we left them a place for the snow in the driveway.

Unfortunately with the amount of snow we get he has to plow that far back in the yard. This is not the city plow - it is the guy who plows my drive. S

o every year I have this space to redo. I may be off on the size of the area...

I like that 👍.

I would repair the lawn and then put up a "snow fence" every fall.

As far as the lawn; from what your describing you have I would cover the surface with bulk mushroom compost, two or three inches, and rototill it in. If it had been a one time thing I would've suggested you use a digging fork in the ruts to get the surface back to where it was. You could fill the ruts in; but there's many years of ruts and all that compression. After rototilling drag a plank, a pipe, an old bed spring to break up the soil and smooth it out Seed it with a good grass seed mix. Never buy seed from a big box store. It's mostly grass seed that is weed seed in your area. The guy who sells bulk mushroom manure may sell seed; Out of a big bin with a scoop and a scale. Cover the seed with more of the mushroom manure, maybe an inch thick. Wait a week, keep it damp, but don't overdo the water.

Grass seed has doubled in price, the last year $5-$6 a pound. But don't skimp on seed. 20 X 50 feet is a 1000 sq ft. Use a minimum of 6 pounds of seed; maybe 10. Don't fertilize the new grass this year. If you do, you won't be able to get the mower thru it. Next couple years use less on that area. It's going to be a thick lawn with some organic matter in the soil for a change.