Tutorials/Starting in the Nether

Obviously there are several ways to take on this challenge.

For the sake of completeness, this tutorial focuses on staying in the nether without any overworld help.

TL;DR: Points to keep in mind

Wear gold so piglins don't attack you! Makes a world of difference.
Immediately find a crimson (red) or warped (blue) fungus biome and convert the fungus stems to wood, then build a crafting bench and craft wooden tools. Now you can mine blackstone (for stone tools), gold ore (everything piglin), and basalt (ghasts can't break it), but not gold blocks (you'll need iron for that).
Don't forget about the blaze spawners, chests, and nether wart in nether fortresses.

The fungus biomes are essential for wood blocks to make a crafting table and wooden tools.
The nether waste makeks it easy to find exposed gold.
Blackstone (to replace cobblestone for stone tools) can often be found around the lava lake level.
Basalt biomes also have blackstone, and basalt is a nice building block that chasts can't blow up.
Nether fortress chests have iron and other epic stuff.

Make gold armor. One piece is enough to convince pigmen you're a good guy. It will save you a lot of trouble, especially in the red fungus biome.

Warped Forest biomes
- Endermen spawn here, not piglins or hoglins. Don't look at them and they'll leave you alone.
Crimson Forest biomes
- Piglins and hoglins spawn here, not endermen. Hoglins drop porkchops, an epic food source.
- Piglins can be bartered with (or rather offerred gold to see what they'll give you). This gives you arrows, obsidian, crying obsidian (for respawn anchor), and fire resistance potions.
Nether Wastes
- Large lava lakes with ghasts, pigmen, and zombie pigmen. Easy to find exposed gold here.
Basalt Deltas
- Polished basalt is a nice, craftable building block which ghasts can't blow up.
- Blackstone is often just under the surface.
- The basalt columns protect you from ghasts while you're working around the area, but beware of magma cubes!
Nether Fortresses
- Build a blaze spawner farm using blocks. Build it 9 blocks down then funnel in by one block each row until you get to a one block hole. Drop the hole down two or three blocks and then leave a one block gap at the bottom so you can kill them and collect the blaze rods. This gives you blaze rods and blaze powder (to make an ender chest with!).
- The chests have epic loot, especially iron (required for mining gold blocks).