A couple of caveats before I get going:

Europe is big, and the medieval is a long period which doesn't have strict boundaries. In addition, games are drawing somewhat indiscriminately from the periods we sometimes call Ancient, Classical, Medieval, Renaissance, and Early Modern pretty indiscriminately. So in answering this, I'm hitting a number of different and often contradictory points, depending on the when and the where.

Looking at your two examples first, London and Prague in 1350 - they would have been very broadly similar, and more so in the cities than in the rural areas surrounding them. England tended to have centralised market towns, whereas the surroundings of Prague would have gone for the more continental tendency to have smaller markets and even some shops in villages.

You probably would not have been able to walk in and buy finished goods, though, even in the cities, unless they were second-hand. If you were looking for new goods, then you would go to the craftsperson in question, discuss what you wanted with them, and have it made. This sounds slow, but it was often possible - assuming you could spend enough - to have clothes made in 24-48 hours, smaller furniture in only a slightly longer time, and so on. Everything was custom-made and custom-fitted - armour in particular. The modern idea of off-the-shelf clothing or armour simply wasn't there.

Food, too, was purchased directly from the producer, with very few exceptions. Indeed, buying goods and reselling them was treated as a crime in many English towns and cities; the overlapping and ill-defined misdemeanours of regrating, forestalling, and engrossing. You could buy raw produce and meat from the markets in the mornings, and then buy cooked meals from various urban cooks in stalls and small shops through the day, or bring them things to have cooked. Taverns would have served pottages or stew and bread, and it might not have been all that wise to enquire quite what was in the stew in London. There usually would not have been much choice on the menu, if any. Bread could be bought directly from bakers.

However... there was also a robust second-hand market. Almost anything non-food you bought could be resold for very nearly as much as you paid for it, allowing for some wear and tear, and this is a thing that is almost alien to us. In the 20th and 21st century, if we buy clothes, tools, books, or the like, we don't have a hope of reselling them, and even jewelry will lose value very quickly. In the medieval and into the Renaissance eras, if you had enough money to buy stuff (as opposed to paying rent and buying food), that stuff did not absorb money; it just held it. This is is, coincidentally, well-represented in games like Skyrim whereby you can load up as many wooden plates as you can carry and sell them in the next village for some amount of money each. The games tend to have more difference between the resale and purchase value than happened in real history, though.

These second-hand goods could be bought from open markets, and from particular retailers who specialised in such things - or direct from the people who previously owned them. If you had money, and your friend was leaving town, it would not be unlikely for you to buy his furniture, which would provide him with money to buy more when he got where he was going, and leave you with either new furniture to use, or stuff you could sell on for the same, or even a bit more money.

Tourist trinkets, bizarrely enough, were almost always available, as pilgrimage badges and the like. These were small, cast metal objects, almost but not quite two-dimensional, which you could buy and attach with a few stitches to a hat or a mantle or the like, to demonstrate the places you had visited as a pilgrim. Some of them were very pious, others were outright obscene.

Depending on what you mean by religious goods, they were not, strictly, for sale. You got them in exchange for donating money to an abbey or church, if you mean things like prayer beads, crucifixes and holy water. Bibles and other religious texts were not available as retail goods, generally - you would need to make special arrangements to have one copied and bound, and they would have been expensive and slow to produce. Nobles gave them to each other as gifts, and they were very often included in inheritances.

Fabric was available in cities in bolts and pieces, and you might either get your tailor to go and buy the clothstuffs from the relevant merchants, or buy it yourself and bring it to the tailor (or to whatever of your servants made your clothes). Plain wool and linen was almost always to be had, silk and other more obscure fabrics less often - but again, certainly in London and Prague if you had the money.

Spices could be bought from specialised merchants in what we would think of as reasonably large amounts. They would not usually be sold by the same people as sold produce, meat, or flour. And pottery (and wooden vessels) were available almost everywhere, and would have been one of the few things generally available off the shelf - they were more or less the same for everyone, and made in bulk, and broken and disposed of in bulk as well.

References:

Shopping in the Renaissance, Evelyn Welch

Europe at Home: Family and Material Culture, 1500-1800, Raffaella Sarti

The Medieval Town: A Reader in English Urban History, 1200-1540, Eds. Richard Holt & Gervase Rosser