Do all the levels in Nethack get generated at Start or are they generated as they are reached

There are four main things that help in hording items: getting a bag of holding, keeping a stash, travel improvements, and value assessment.

Bag of Holding

These can be purchased in tool shops and other stores, can sometimes be found lying around in the Gnomish Mines, and there's a 50% chance you'll get one at the end of the Sokoban levels. Refer to this map for reaching the Mines and Sokoban, but simply put they're fairly early. The earlier you get one, the easier everything becomes.

The bag of holding is a container, which automatically expands your carrying capacity. Unlike your inventory which is limited by the number of letters in the alphabet, an infinite number of items can be stored in a container. Of course, an infinite item quantity is an infinite weight, which is where the second benefit comes in that a bag of holding reduces the weight of its contents. An uncursed bag of holding reduces the weight of items by 1/2, while a blessed one reduces the weight by a whopping 3/4!

Bags of holding make it a lot easier to both carry all the essentials you need to survive in the dungeon, as well as traffick heavy goods across long distances. Hope to get one as early as possible. However, there are some dangers involved with what you put into a bag of holding: read up on them here.

Keeping a Stash

It's indeed unreasonable to try and carry everything you can. So what is important is to have a place to safely store your stuff. Keeping a stash often is tasked with a few points.

1. Scare monsters away - monsters that might pick up your stash items can be scared away by either dropping a scroll of scare monster on the stash, or by engraving "Elbereth" onto the ground. Ideally Elbereth written permanently via a wand of fire or wand of lightning. (Since 3.6.0 though, Elbereth only works on the square you are standing on, not on stashes.) So use one of these, or hostiles can do things like pick up and use your weapons, wands, potions, etc, or more dangerously gelatinous cubes can eat all your stuff.
2. Use a container - Not every monster respects Elbereth, and the majority of creatures that don't happen to be the kind that pick stuff up. Storing it in a container prevents these creatures from accessing your stuff. Pick something like the many chests you see lying around. Just be warned that most containers are of an organic material which gelatinous cubes will eat, destroying everything inside - so don't forget Elbereth!
3. Keep in a safe place - Elbereth and containers only protects against creatures themselves, not stray bolts of energy. You want the stash to be in a place that will ideally see no monster activity, or not be in danger of damage. Many people pick the first level of Sokoban, as its monster spawn rate is very low (and the Eye of Aethiopica artifact provides a very quick warp to Sokoban when Invoked). An alternative method is to store your stash in a one-tile room behind a locked door. Also consider using boulders, which block most monsters from accessing it.
4. Keep easy access - Don't create a stash in a remote place if you can avoid it. Instead, try to stash it as close to stairs while still being out of the way of combat. Combine this with mining short-cuts through levels if you have a pick axe or mattock, and it'll be a lot quicker to return to the stash once you have better identification methods.

These are the main points of stashing. All it needs to do is hold onto items and keep them safe.

Travel Improvements

Keeping a stash is worthless if you can't use it! You need to have better methods of travel across the levels. This isn't really limited to hording items, but it's something I can cover as a relevant tangent. Just consider 3 commonly accessible methods of easing your travels (I'm not going to cover the Eye of Aethiopica since it's rather specialized and already covered up above).

• Level Teleportation - One of the best methods to reduce travel time is level teleportation. The easiest method is by reading a cursed scroll of teleportation. Combined with teleport control in some fashion, this lets you very quickly reach the level that your stash is from, and then return to where you need to be. Very risky without teleport control, however.
• Teleportation - Standard ease of travel when moving across a single floor. It can also speed up actually reaching your stash, and then returning to the stairs. Not as risky without teleport control, but can be more annoying and time-consuming.
• Digging - Pick up a pick axe or dwarvish mattock, and just start taking out walls. Convert as many floors to a straight line path from stair-to-stair. The less corridors you have to navigate, the less resources spent. While digging holes to fall is an option, do note that where you actually drop is random so building a complex "down elevator" doesn't quite work as well as it may seem in theory.

Value Assessment

The final point to knowing how to effectively horde items is knowing what to horde. Equipment, such as weapons and armour, are often useless to keep. They sell pitifully compared to their weight, and you rarely need to keep any equipment that isn't immediately useful to you. Also try to figure out the usefulness of items by unconventional means. Reduce not just how much you have to carry, but how much you need to stash as well.

And finally, consider carrying no more than one copy of heavy items like potions when unidentified. Identifying one serves to identify them all, and simply rely on one or more stashes to keep the extras.

I've finished my game for the wizard so I can outline the strategy which was working for me. I don't know what parts you know exactly, so I will tell you everything I consider important.

First of all, dump your quarterstaff and try to use daggers as your main weapons. They can be not only wielded, but also thrown, and if you become skilled in using daggers, you will be able to throw several daggers at once. Ten daggers or so is a good number to start with. Also I'd find an armor which doesn't hinder spellcasting (like studded leather armor) and try to enchant the cloak. Obviously enough, you should try to learn as many spells as possible and get all the resistances you can.

I advise not to go into the Gnomish Mines when you find the entrance. You can reach the Minetown easily, but you won't be able to reach Mines End yet and get out safely. So instead of going to the Mines, go to the Oracle and then to Sokoban. Sokoban should train your strength because you will move boulders a lot, which is helpful, and also you will get some gold and a gift at the end, which is, as you probably know, either bag of holding or the amulet of reflection.

After Sokoban you should go to Minetown and try to reach Mines End. Minetown has an altar and if you're lucky, it will be your god's altar. If that's the case, you should offer corpses of recently killed monsters to your god until you get Magicbane. This is a magical dagger, which is extremely helpful in combat.

Mines End will give you a luckstone (and also some gems). You have to fight a lot of monsters there though, so stand on the stairs and use Elbereth to keep them off. If you have Magicbane, engraving done with it will be harder to erase.

If you have survived Mines End, you can return from the Mines to the main branch and safely descend until you come to the level with the quest portal. Don't worry, if you haven't reached level 14, the first quest level usually has Wraiths whose corpses raise your level when eaten. If you still need to gain levels, descend lower in the main dungeon. Usually I don't linger in the level after I have explored all the passages. You should aquire necessary level before you reach Medusa's island.

When your level is enough, you can finish your quest. Your nemesis won't be tough if you know how to hinder his healing. After you finish him, you get your quest artifact which replenishes your power, and later on you shouldn't have any problems.

That's the basics of the wizard strategy.