OK, so you already have a Raleigh Wayfarer and like the way it rides. Don't start laughing now, but let me say this; a Wayfarer, by 3-speed roadster standards, is actually quite a sporty bike!. The weight, give or take, is 35 lbs and they are built on the Raleigh Sports frame which has quite nimble handling. They're no racers but they aren't tanks either.
The kind of traditional roadsters you are contemplating, sometimes referred to as "Dutch bikes" are usually quite a bit heavier, have bigger wheels, longer wheelbases and slacker, more ponderous geometry. Comfort-wise in a straight line - great. Handling on twists & turns and the amount of effort required to get one up a gradient - not so good.
I would think very hard before buying something like a Pashley or Gazelle with 28" wheels. They look nice and traditional, but they are best suited to flat terrain, as they lack the very low gears of a triple-equipped hybrid or MTB that takes the pain out of getting a heavy bike up an incline.
I've given quite a bit of thought as to what I would like from a 3-speed and for me it comes down to practicality and low maintenance but without excessive weight. The problem is, the lightweight end of the 3-speed market has pretty much become extinct. What's left is the heavy end. My intention is to build a lightweight 3-speed from a 1980's 531 tourer frame I have and fit as many alloy components as possible. That should give me the practical qualities I want but still be fairly sprightly. I can't buy such a bike new any more though, so my only option is to build one DIY.