So what is the best place in the rynek to enjoy a beer on a Sunday afternoon, and what qualities make it the best?
I know you asked about Rynek, but you know, Rynek is for tourists...
If you are looking for good selection of Polish beers and some Czech beers try pubs near "nasyp kolejowy" = embankment of rail. It is not grand place but there is a collection of cosy pubs there, for example this one with Czech beer:
Those are mostly pubs so decent food is harder to get but regular stomach can handle food from this place:
As I said, it is not grand area (it is planned to became a pedestrian zone in a few years though), there is a construction site of a theater next to it, but it is quite close to the Rynek and somewhat "off the bitean track" place.
One more thing, trains are running under your head there, but this is kind of special feature of the place ;)