First of all, I completely understand the popularity for CJs. Their beauty and player power speak for themselves. If that's all you care about, then they are a clear front runner.
I side with whoever first proposed the idea that it would be nice to have a different era represented, however. CJs are too close in issue to T206s, so there's far too much player overlap.
Several of you take issue to including a set that can never be completed (yet each of the Big 3 share this problem for most people's budgets). So, where do we go from here? Have E120s been suggested? A decent-sized set which is shoehorned in between T206 and 1933 Goudey. A great HOF selection and it offers many wonderful obscurities if you like that sort of thing. Aestheically pleasing, and the design is certainly representative of its era. Here we have a bunch of Roaring 20's players who straddled the Deadball and later eras. As with the Goudeys, you can even collect their Canadian counterpart should you wish. If you're into even more parallels, you'll be kept busy! There's a lot to like with this set.
I heartily disagree with any post-1950's suggestions due to their "youth" and overabundance. Give it time; perhaps it will make sense later on. I definitely don't want to hear the word "refractor" in this discussion at all!
But your picks are your own. Everybody has the right answer (for themselves).