I have a long and step drive way, both side are washing off

I'm guessing you mean you have a steep drive (acute angle) and you're getting soil runoff. Plants will probably not work for you since they'll be washed away, too. I would suggest using a plastic or cloth mulching material that you can cut and pin down and then using a decorative rock (not gravel) to keep everything in place. Only go as wide as you need - say about 12 inches on each side. That should solve your erosion problem.

Best plantings are really very regional. Weather, soil type, etc.

Go to a local real garden center and ask their advice and maybe buy a plant. Show them a photo. That helps them a lot.

You can then check your local HD or Lowe’s and see if they carry something the garden center suggested for less.

The garden center more likely to bargain for a quantity buy.

Try railroad ties (I think that’s what you call those large wood beams they use) and place them into a stepping pattern, that way your ground won’t wash away and you would be able to plant anything you want.

I would look into ice plant. Very sturdy, their roots connect under the ground and you get a pretty fast result. But yes, something "non organic" for the interim might help. Here is a link on all things ice plant.

https://www.google.com/search?rlz=1C1BLWB_enUS700US700&tbm=isch&q=ice+plant&chips=q:ice+plant,g_3:ground+cover&sa=X&ved=0ahUKEwjixaOwuYrbAhUJKWMKHbgfDpoQ4lYILCgA&biw=1164&bih=559&dpr=1.38

Hostas are my go-to tea plants for quick bordering and in gardens Empire beds