Just to get it out of the way everything in the suspension on a 38 year old car probably needs to be replaced. It will undoubtedly handle better if you do the bushings, end links, ball joints, wheel bearings, and springs. That said it is also a 38 year old luxuary car. Its also one of the last Mercedes with semi trailing arm rear and a suspension designed around bias ply tires. When new it was supposed to be soft and its not going to compare to a 911 or E39 without modification.

If it were a w124, W201, or 107 I'd know what to use from the merc parts bin to make it a bit sportier. Like anything though I'm sure you can get some larger wheels (16") for less sidewall, cut stiffer springs with big sways from a heavier car with similar suspension, and go with bilstein HDs which is essentially what I've done to my 124. One possible source of parts that comes to mind is the W126 (someone who knows better should chime in). I'm sure there is info out there.

To answer your question in your title you do have your work cutout for you. I'm normally not a fan of it when people say "you bought a Mercedes not a Corvette" but my dad had NA 300D 123 when I was a kid and they do move around a lot.