An edging of some sort-plastic, metal or cement

While lining the edge with a raised material is a common solution, it is not a good solution. It looks bad sticking up -- usually really bad -- and sometimes physically gets in the way. The problem to begin with is that the soil is the same level as the pavement. It should be about 2" below. You could remove soil in an 8" swath (x 2" depth) next to the drive, then taper/blend that elevation to the existing grade. The tapered area need only be within a swath that extends 2' from the edge of drive. It's not necessary to blend/change the soil elevation directly below each plant. Since that portion is unseen, it won't matter. After removing the soil, add mulch over the whole bed (except below the plant).

Over a period of time. the foliage of the plants should expand and grow together. As it covers the soil, it will no longer be necessary to add mulch.

Another thing that will help reduce weeds (a lot!) is Preen. Many people try it and give up because they don't think it's effective. It seems to me that the first application needs to be a little heavier than called for in the directions, or a second application needs to come sooner than called for in the directions. After making that adjustment, it seems to do a great job of keeping newly sprouting weeds at bay. It will not do anything to get rid of weeds that already exist. They must be dug out by roots or poisoned individually.