This is a very basic question, but I'm a very new DM and I can't seem to find any indication how characters acquire mundane weapons and items beyond their initial equipment. I know some items they can discover in treasure caches, and I figure I could put weapons there as well. But can players buy weapons? Do they need to find a merchant selling the weapon they want or do they just deduct gold from their holdings and assume the items?
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This is entirely up to you as the DM!
Typically, after each session or adventure, the characters return to some sort of a town. Depending on the size and wealth of the town, you can limit the availability of certain items. If you run a more casual campaign, you can just let players deduct the gold from their coffers and purchase the item without any roleplay.
Keep in mind, however, that limited items can be an important plot point. For example, a journey through the wilderness can be made much more realistic if you point out that they won't have any stores to buy or sell from on their journey.
Sorry to drag you back to the real world, but think of how you acquire items in the real world ... players can buy whatever they like (within reason) assuming they have access to a source.
So if you need a piece of rope ... you go to your local hardware store, or you pop next door to a friendly neighbour and see if they have some you can buy (lend).
But if you're at the bottom of a cliff, trying to get to the ruins of Kazak perched high up on a ledge, then you hope someone planned ahead ... or you keep your fingers crossed that the merchant caravan you passed earlier in the day has got some.
Neither answer hits the RAW approach here so let me give it to you:
The DM guide and the RC are largely silent on how purchasing works beyond some general guidelines and this is intentional, they leave that up to you. However, there are several built in RAW ways to acquire magic items in 4e and a lot of it depends on setting, enchantment, and item rarity, let me address all of these things.
Now, you mentioned the possibility of including magic items/weapons in your treasure drops, if you aren't already doing this you might want to look at how your doing treasure. If you're not rolling treasure parcels I highly recommend starting. There is a table in the back of the Rules Compendium that gives you 4 lines to roll treasure, this allows you to create random treasure parcels tailored to your PCs' level. The last line of this determines the magic items dropped in the parcels, it even builds in item rarity (common is an odd roll, uncommon even, rare 20). Some suggestions:
If you want to include mundane equipment or weapons into a treasure parcel add it wholesale or substitute it for some of the gold.
Finally, keep in mind that the math of 4e is heavily dependent on your characters having the proper equipment, if they don't they will be ill prepared to face the challenges you present. A PC should pick up a new magic weapon or implement ever 6 levels or so (this is the rate at which the enhancement bonus changes), and a new set of armor and new neck slot item at about the same rate. This can come from either finding that item, purchasing it, or using gold to enhance their current enchantment through the
Hope this helps expose some of the RAW mechanics of treasure awarding in 4e and that you have a great time.
A TL:DR for those just looking for the answer to mundane equipment: