Hi, so to follow across from the other thread about bread, we also have some depictions of 'wet' goods in contemporary illustrations and illuminations. Many depictions of market scenes show that poultry in particular was sold "whole" to be plucked and dressed at home. Meat when not sold on the rack is likely to have been stored in ceramic pots or in metal trays, or simply wrapped in cloth if cured and preserved. A great amount of medieval meat was preserved rather than eaten fresh, so was likely to either be dried or salted, and thus likely stored in jars. Significant archaeological evidence from the burh at Stafford shows that the meat that was produced at the mass butchers there was indeed stored and distributed in ceramic vessels produced on-site.
Sherd evidence suggests that pottery usage was commonplace across urban scenarios so it's likely that you could purchase suitable storage vessels at a market if you lacked your own. Some Stafford Ware sherds show up in Chester and Dublin, suggesting that these ceramic jars and amphoræ were being used - or reused - for the export of (probably) meat.