Sounds to me like you want to keep some space and visibility a few feet around the edges of your driveway. Plants that are low growing are good for that. There are even species of grass that don't grow very high. I personally prefer native plants.

My drive is not as long as yours but I have a similar situation. For the last five years I have been planting daylilys and ornamental grasses along one side. I add about 5 more feet each year. I add mulch to the newer areas, the areas that I established five years ago are now thick enough to keep out most of the weeds and I don't do much to those areas. Maybe you could do some drifts to break up the long driveway?

We have eastern red cedars that are on the south side of the driveway and although I love the cedars for the birds that they attract they are a problem in the winter as they block the sun and any moisture on the driveway stays frozen.

Also there is a fescue that only gets 6" tall, it grows in clumps and multiplies by runners. It would take some time to get it established but after that you wouldn't even have to mow. It is very invasive though.