Let's identify what is needed to "sustain a living" in minecraft, provided this living is more then standing still in a hole. Basically the things you want to carry around with you all the time in a survival world or that you want to accumulate quickly in a base you set up in a new world.
First of all: Food. Keeps you be able to run, jump and fight, regenerates health qickly (as of 1.9+) and is needed to survive longer then until you starve to death. to get this take two stacks of eggs with you as well as some redstone materials and build up a fully-automatic chicken farm that will provide you with cooked chicken (and feathers).
Then: All the tools and armour. You need a sword, pickaxe and shovel in the nether (axe not really necessary) and the four armor pieces would be nice to have. A bow is quite important as well.
- There is one easy way: Make good diamond gear in the overworld, put the Mending enchantment on it and take it with you. You will then be able to repair it with XP directly, therefore it will never break if you are careful.
- If you don't have mending, then you would need to repair your tools or make new ones all the time. Repairing costs diamonds (or iron if you opt for iron gear), so you would need to bring large quantities of those with you but you would be in trouble as soon as the supply runs out. There ain't no diamonds in the nether (see footnote at end)! You could maybe bring a villager with you that trades emeralds for diamond gear, but you wouldn't get all the gear from him (maybe enough, though). A source of emeralds are other villagers that could trade coal from wither skeletons, gold and rotten flesh from zombie pigmen, or drops from animals you would have to herd in the nether and bring with you from the overworld (wool from sheeps, lether from cows, raw chicken and raw pork).
- If you don't want to maneuver a villager through the portal into the nether your only chance lies with taking saplings and dirt with you to grow trees - giving you a sustainable source of wood - and make sticks for tools from that. As a main material for the made tools you can use wood or gold from zombie pigmen. I'd go with the latter. And maybe diamond tools every once in a while when you find diamonds in a nether fortress chest.
To properly use your tools and armour you could take an enchanting table with you and enchant them after you made a new tool. Lapis Lazuli would run out sooner or later though. If you bring a cleric villager for trading gold and rotten flesh for emeralds with you anyways, you could trade lapis lazuli from him.
As for a bow, the only way other then to bring an ample supply of string with you would be a fletcher villager that trades emeralds for a bow and for arrows. Otherwise you'd get feathers for arrows only from chickens - a stack or two of eggs would suffice to get a chicken farm going. Flint you can get from the gravel patches in the nether.
Then there is smelting. Bring a stack of furnaces with you so you never run out of them if you loose some (no stone available!) and bring a bucket with you. You can use a lava bucket as fuel or coal from wither skeletons or blaze rods. You need to smelt stuff, as the only solid (ghast-blast proof) material you can get easily in the nether is nether brick and this is a lot easier to get by smelting nether rack. Also, you may have to cook your food.
That's pretty much what I can think of at first. To re-iterate what you should bring with you in case you make your stuff yourself in the nether and don't have mending-enchanted gear to bring with you and also if you don't bring villagers or animals with you:
- several stacks at least of dirt (and at least one grass block if you want it lush and green in your nether base - remember, you will never see the sun again!)
- saplings, best is spruce I find (plant them in a 2x2 pattern)
- two stacks of eggs (to be safe), should yield at least one chicken from which you can create more
- some redstone supplies, for an automatic chicken farm and maybe everything else that comes to mind later (if compressed into redstone blocks you can carry quite a lot with you in one single inventory slot) - and a stack of stone for repeaters and comparators!
- enchanting table and 15 bookshelfs, plus a stack of lapis lazuli blocks (enough for 192 tier-3-enchantments)
- a stack of string for bows (invaluable in the nether against both ghasts and blazes!)
- furnaces and at least one bucket (better just to bring a stack of iron blocks)
There is only one very important thing left: Bring a bed with you and once you are in the nether take a short nap! (just kidding)
footnote: In fact, there are: In nether fortress chests. I would deem this as a too scarce source of diamonds to repair your tools, though. And hoping for zombies to spawn as a zombie siege when killing zombie pigmen and hoping for them to drop an iron ingot will also yield far too little resources.
