This is ultimately the most important factor when selecting shocks. The wheel rate and the shocks dampening capability have to be in the same ballpark.
I am currently using Bilsteins with factory undersized bars™ and they work really well.
I do plan to get thicker bars (and maybe even sway bars) one day, but until then, what I've got is completely acceptable in a 60 year old car. The made the ride smoother, tighter, firmer, and even made the car corner better.
So, while I agree that a good spring rate is important, if you're going to start by changing only one thing, I'd change to Bilsteins first.