Go slow. Get up under the car and verify exactly what parts need replacing.
From my experience both the thrust arms (rear, diagonal) and the front tie rods and tie rod assembly can easily contribute to this type of handling problem. Of course there are more items than can as well, but try these first.
Often, especially with the miles on your car, you won't need as many parts as you might suspect.
Keep us posted,
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)