What provisions to take to particular dungeons (Cove, Ruins, Weald, Warrens, Darkest)?

From personal experience I would suggest as a baseline a bit less food since you usually find some (at least for short ones), same with torches (6 for small), and a 1 of everything else. Next, based on DarkestDungeon Wiki - Curio you can estimate what extras you need given where you go:

• Ruins: + Holy Water, + Skeleton Key, + Shovel
• Warrens: + Herbs, + Holy Water
• Wield: + Antivenom, + Bandages
• Cove: + Shovel
• Crimson Court: +++ Shovels, + Herbs (thanks, @ZealousHypocrites)

There's no simple, straightforward answer. It depends on what you want out of a dungeon.

Obviously, you'll always need Food and Shovels. Torches are optional. I find that when playing with Torches and Food, bring lots of both if you want to benefit from Curios more. (You should snuff out your torch completely before looting any curio and before a battle ends to increase the loot gained). So ideally you want 4 torches per battle beyond the first.

Typically, a short dungeon has ~4 battles, a medium ~8, and a long about 12, so you would want 12, 24, and 24 torches (counting the firewood as 4). I find that in long dungeons, you don't really need more, as you don't need to snuff the torch for extra loot, you'll have plenty without doing that (and save the 75 gold).

I personally always bring the maximum amount of food. It's quite often not enough, even in dungeons that normally drop a high amount of food from Curios (Cove, Weald). The binomial distribution with typical Darkest Dungeon parameters for food has a long tail. For example, using N=100 tiles, P = 5% chance of a food tile, the result is an average of 20 food needed, but the 95% interval is at 40 food needed. Bringing twice the average amount is a good rule of thumb.

Note that even if you're not intending to use any torches for light, if you want to use shambler altars, you'll need to bring at least one torch.

Curio Provisions

First, what curio provisions you want to bring depends on the length of a dungeon. In a short dungeon you will have room for most of the loot you'll ever find before the dungeon is complete, so you should bring every curio item you can. In a long dungeon you should really only bring those curio items that can give you benefit without using up inventory, by say buffing your party or curing a negative quirk. The one exception is extra food (which you sometimes need) and the one skeleton key for the secret room, easily increasing your haul by 5,000 over bringing just gold back.

That means the following list (in addition to the standard amount of food, shovels, and optionally torches): Each entry is for a random Small / Medium / Large dungeon.

+---------+-------+-------+-------+-------+--------+---------+-------+
| Dungeon | Keys  | Water | Herbs | Antiv | Shovel | Bandage | Torch |
+---------+-------+-------+-------+-------+--------+---------+-------+
| Ruins   | 3/4/1 | 3/5/2 | 3/5/0 | 0     | 0      | 0       | 0     |
| Weald   | 2/3/1 | 2/3/4 | 2/3/2 | 2/3/0 | 1/2/0  | 2/3/0   | 0     |
| Cove    | 2/3/1 | 1/2/2 | 3/5/7 | 0     | 2/4/0  | 0       | 0     |
| Warrens | 2/3/1 | 3/4/2 | 2/3/2 | 0     | 0      | 1/2/0   | 2/3/4 |
+---------+-------+-------+-------+-------+--------+---------+-------+

This chart contains my estimates done by some trial and error. Todo: write a program that loots some large number of random dungeons to find the actual optimal values later.

If you have an antiquarian, increase the values to this:

+---------+-------+-------+-------+-------+--------+---------+-------+
| Dungeon | Keys  | Water | Herbs | Antiv | Shovel | Bandage | Torch |
+---------+-------+-------+-------+-------+--------+---------+-------+
| Ruins   | 3/5/7 | 3/5/6 | 3/5/6 | 0     | 0      | 0       | 0     |
| Weald   | 2/3/5 | 2/3/4 | 2/4/6 | 2/3/5 | 1/2/4  | 2/3/5   | 0     |
| Cove    | 2/4/6 | 1/2/2 | 3/5/7 | 0     | 2/4/6  | 0       | 0     |
| Warrens | 2/4/6 | 3/5/6 | 2/4/6 | 0     | 0      | 2/3/5   | 2/3/4 |
+---------+-------+-------+-------+-------+--------+---------+-------+

The reason is of course that the antiquarian gives you bonus loot with each curio you open. You really want to get every single one. The best strategy is to walk the dungeon twice, first to find out which ones you got, then another time to grab them in the best possible order.

Battle Provisions

If you want, you can bring provisions to make fights easier. Especially in Champion and Darkest dungeons, provisions can help you cope with the extremely challenging content. You run these dungeons to complete them, not to obtain loot, as the much easier veteran and beginner dungeons give comparable amounts of money for far less trouble. This table ranks the usefulness of the provisions in battle (besides torches, which are useful everywhere for easier battles). It's largely dependent on the frequency of the things the provision helps with multiplied with how severe they are. For example, the cove contains a moderate amount of bleeds, but they're all very powerful, thus bandages are great there.

Low: The provision helps rarely, and when it does it's not all that amazing. Ex: Laudanum against the Madman. You usually prevent 8 stress with each bottle used.

Medium: The provision is useful and the conditions are quite frequent.

High: The provision helps a lot with preventing common conditions that are very dangerous.

+-----------+--------+--------+--------+----------+---------+
|  Dungeon  | Water  | Herbs* | Antiv  | Laudanum | Bandage |
+-----------+--------+--------+--------+----------+---------+
| Ruins     | low    | medium | none   | low      | low     |
| Weald     | medium | high   | medium | low      | low     |
| Cove      | medium | low    | none   | low      | high    |
| Warrens   | high   | high   | low    | low      | low     |
| Courtyard | high   | medium | low    | medium   | high    |
+-----------+--------+--------+--------+----------+---------+

*Assuming you have one of the classes that likes to debuff itself, Herbs are amazing to always have available. Three classes with self debuffs are the Jester, the Flagellant, and the Hellion.

If you have a Plague Doctor, who can heal Blights and Bleeds, Bandages and Antivenom are less useful.