Minecraft wiki entry for Hardcore_mode, associated text: Enchanted Golden Apples can make the first travel to the Nether a lot safer because you probably don't have any Potion of Fire Resistance, and the Apple can provide 5 minutes of fire resistance. Try store at least one in your overworld exploration to use in your first travel to the Nether, and when inside of a Nether Fortress, use it to help you against the dangerous groups of Blazes or use it in any emergency, like Ghast's knockbacks. Remember, you can only respawn in Spectator mode.
At least one piece of Gold Armor must be worn to prevent piglin attacks.
Gold ingots can be used to barter with piglins to obtain fire resistance potions and ender pearls, as well as other items.
Diamond sword, iron armor, and pickaxe. (Iron pickaxes, or better are fine, but they shred netherrack very fast.), bow (and at least 32 arrows, unless it's enchanted with Infinity). Make sure to enchant everything with 1-skill-point enchantments. It barely costs anything but can make a difference.
Flint and steel, to relight deactivated portals. If you find yourself without one, they can sometimes be found in a nether Fortress.
At least 16 Wood. You can chop down huge fungi for wood if you are near a Crimson Forest or a Warped Forest. Bones can also be brought to these locations to make Bone Meal, both for growing huge fungi and generating additional fungi. However, starting a wood farm outside of the respective biomes will require Silk Touch, as fungi will only grow on the matching nylium type.
If you are not near a Crimson or Warped forest, you can bring some Bones, dirt, and saplings. This way, a tree farm can be started (ideally in a protected location, as trees are flammable). Making a wood farm this way is also easier, as it eliminates the need for both Silk Touch and bone meal, although the latter can still be used to make the trees grow faster. If you run out of bone meal, you can kill Wither Skeletons for their bones, but this is highly risky and not recommended as it requires finding a Nether Fortress, and you will likely also be facing Blazes in doing so.
Any iron ingots, coal and food (Remember, you could only respawn in Spectator mode.)
A stack or two of cobblestone as an emergency blocking material. Ghasts can't destroy cobblestone.
A stack or two of sand or gravel might be handy for climbing down sheer drops. Be careful: getting shot off the top of a pile while descending is usually fatal.
A cauldron, because you can actually place water in cauldrons, so if you accidentally set yourself on fire, you can quickly extinguish yourself by jumping into the cauldron.
A bowl, to make mushroom stew, which is highly recommended due to being the only secure food source in the Nether. It can mainly save you from starving because it's very useful if you couldn't find your portal anymore.