How do I determine precisely what each merchant the players encounter will have in their inventory?
Does one usually allow merchants to have all items from the core rule books in stock, or do they create a list for each merchant? Or is random generation a better option?
In a medieval/low tech setting I almost never allow full access to all items in the equipment list, because:
When the characters walk into a given merchant's shop, I generally let the dictates of the story determine whether the objects they seek are on hand. If it interrupts the flow of the story to have the characters run all over town looking for something, it's better to say the merchant has what they need. But if it feels right to spend more time on it, I let some of the elements above seep into their search for gear.
For industrial or post-industrial settings, I generally allow items to be easily found, and I don't worry too much about price. That said, you can have some fun with defective goods, as long as you don't overdo it. Introducing something like the non-functioning pistol Boris the Blade sells to Tommy in Snatch is a dirty trick for a GM to play, but sometimes it's appropriate.
This really depends on what your setting is, and what kind of items you want to be available to the players.
The rules as written suggest that PCs should be able to find mundane and common magic items just about anywhere, and that uncommon and rare magic items cannot be bought and must be found through adventuring.
However, this should not preclude you from either limiting the availability of specific mundane or common magic items, or allowing your PCs to purchase specific uncommon or maybe even rare magic items.
Some guidelines:
It should be relatively easy to get mundane items. If you can't get a specific item, or class of items it should be related to the plot not just some kind of random DM fiat.
Make your availability make sense. A small town shouldn't have a huge stock of magic items (unless there is a really good reason) and a big city shouldn't be totally devoid of magic items (unless again, there is a good reason).
Make your players work for special stuff. If they want a rare or uncommon item you might allow them to get it, they just have to work a bit harder for it than just walking into the store.
This is just some general advice on item availability. It would probably make more sense if you gave some information about the setting you play in, or the general magic level.
In general stores:
When a player wants any of the common goods (soap, a candle, a bedroll), the general store basically has it. Sometimes I will throw in story elements "A bedroll? I have a few moth-eaten blankets, but if you go down the road to Ms. Murphy, she makes wonderful bedrolls". Of course, Ms. Murphy has a side-quest the players can spend an hour or 2 on for a break from the main quest.
In specialty shops:
In a true niche store, either there will not be much stock, or there will be bogus stock. In a magic store in a low-medium magical setting (like in Shadowrun, there's enough magic for stores, but it's not ubiquitous like it is in some games/settings) there are likely useless fetishes, charms, and similar things for the gullible to buy and think work, but the proprietor likely knows all the magic-users in town and has a box of the "good stuff" whenever those magical folks come in looking for a new magical item/accessory.
In a more "general" specialty shop, they will have what makes sense, and refer any other business to either another specialty shop, or the general store down the street. The stable will sell horses, mules (and other beasts of burden), their tack and saddles, but pretty much nothing else. The Smithy will stock horseshoes (because he makes them), and weapons, but won't likely sell/fix saddles... that's the something the livery should be able to sell/fix.
