Lessons learned from my first successful amulet run:
Follow the guidance in this strategy thread; it helps greatly.
Horde all potions and scrolls till level 8 or 9. If possible, don't drink or read any till then. If you run out of pack space, drink a few potions but don't read scrolls yet. But make sure you drink and read before you hit levels in the teens, as that's when things get really serious.
Gather as much equipment as possible, but avoid putting or armor or rings or wielding the weapon until you're ready to read through all the scrolls.
As you acquire weapons, throw them at low-level mobs, like bats or kestrels. On a hit, it will tell you the weapons +#/+# stats. Anything with a negative number is cursed. Throw it away.
Keep a thrown weapon or stack of ammo with you the whole game. Throw weapons at mobs whenever you have a chance. You can keep your melee weapon wielded and throw other weapons by going into the inventory screen. While using a bow or crossbow does add additional bonuses to the ammo, I have yet to find one good enough to outweigh using a melee weapon. Besides, the turn you waste re-wielded melee as the mob gets adjacent is more valuable.
Once you enter a new room or hallway, throw a weapon into it. It will give you an idea of how big or long the room or hallway is. You also may hit a hidden monster, giving you time to prep, run, or throw weapons.
When exploring room, wield flaming or blessed weapons, as they add another square of vision in all directions. As soon as a mob approaches, swap back to your weapon of choice.
Once you reach 8 or 9, find a quiet room and drink all your potions. There's no real good strategy to this, as its blind luck. I generally start with single potions I have, then save the stacks for last. Typically, you'll have singles or the rarer/more potent potions, and multiples of the more common ones, such as healing potions.
Try to avoid reading scrolls until you have a good set of armor and a good melee weapon. The goal with the scrolls is to enchant your weapon as much as possible and hope for a vorpalize scroll. For armor, you want to enchant is as much as possible and hope for a protection scrolls to make it rustproof.
For armor, ideally you want one of the armors with a special effect; Elfin Mail, Shozoku, or Spartan Curiass. If you have a choice, the spartan armor is the best, as it will give you an extra strike about half the time you attack. This will make child's play out of tougher mobs like trolls.
For weapons, try for one of the higher-count damage dice weapons; longsword (2d5), 2-handed sword (4d4), battle axe (5d2), war hammer (6d2), or katana (4d3).
As you get identify scrolls, save them to use on rings and staffs/wands. Rings take priority since you can only identify them by scrolls. Wands and staffs are second priority, but they can be identified by zapping a monster and wasting a charge. Weapons can be identified by hitting a mob, either melee or thrown. Armor is identified once its worn.
Wearing rings increase your appetite, so wear them with caution. Its a good idea to keep several beneficial ones around for different situations. A stealth ring is a must for levels below 20.
On levels 1-19, search every room, kill every monster, and find all the treasure possible. Once you get to level 20, it becomes a game of survival and evasion. Only kill things on the lowest levels when you are certain you can win before you start fighting. If you get cornered, stand and fight; you will be surprised how well you may do.
Horde paralyze wands and potions for levels 20 and below. These are critical to surviving attacks from griffins, dragons, medusa, and such. If you have to fight a nasty mob, pound away until you are about to die, then throw or zap it with paralyze. You can back off and heal or rest until your HP is full. Then you can either finish off the mob or run away.
There are a few ways to instant-kill most mobs. Potions of demolition and instant weapon will vaporize most mobs instantly. Instant weapon is especially good for this, as it leaves behind high-level bonus weapons.
Nymphs steal the last item in your pack, so keep something you won't mind loosing on the bottom. Items you pick up are added to the bottom of each grouping. If you want to take a grouping out of the middle of the pack, you have to drop all items in that group. Once you pick them up, they will rearrange on the bottom of the list.
As you acquire more stuff, you will want to throw away useless items. Generally, once you have a good enchanted melee weapon and armor, you want to carry a stack of ammo or a couple good thrown weapons. Leave behind all other bonusless weapons, as they'll just clutter your pack. Once you get rustproof armor, you can leave all other armor sets behind. Likewise, drop cursed items as accidentally wielding one could cost you a game.
Every item you carry should do one of these things:
1. Keep you alive (healing, food)
2. Allow you to escape (paralyze, confuse, teleport, stealth)
3. Kill mobs (demolition, instant weapon)
4. Help you explore (clairvoyance, mapping, disarming, light)
5. Deal with conditions (remove curse, restore strength)
If you are about to die, you need to weigh your chance of escaping or healing. Use items to save your life (i.e., this may be your last action) in this order:
1. Can I teleport away?
2. Can I paralyze the mob and escape?
3. Can I try to instant-kill the mob?
4. Can I confuse the mob and escape?
5. Can I heal myself?
In an emergency, removing yourself from a fight is your first priority. Second, remove the mob; no monster, no death. Healing yourself is last priority. If you try to drink healing potions while a monster is beating on you, you will only delay the inevitable.
Another emergency technique is randomly zapping the mob with wands and staffs. Yes, you may make the situation worse, but there's also a chance you may instantly kill or neutralize the mob.
A great last ditch escape method is to keep a ring of teleportation in your pack. Yes, it is a cursed item, but it will save your life. Ideally, you will want to keep a scroll of remove curse, too. That shouldn't be too hard, as you shouldn't have had to use one if you have been smart and methodical about identifying your items and not haphazardly putting on gear. Once the mob is about to kill you, and you are all out of the other options, don the ring and run. Hopefully your random movement will teleport you out of danger.