Class
Unlike retail, if you want to be a goblin you're class choice is gonna matter. Grinding/farming is way more effective of a gold making strategy in vanilla than retail due to the higher relative vendor price of greys as well as green/blue items (not including disenchanting). There is really on 2 classes in this discussion: Hunter (which you'll use to solo dungeon content you shouldn't normally be able to solo) and mage (which you'll use to aoe grind a bunch of grey items to vendor). Now based on what we know, Dire Maul North Tribute runs being soloable by hunters is blizzlike, and if this is the case, hunter is the clear choice for the class to choose, at least only in terms of gold making opportunities. As far as raiding is considered hunters suck.
Leveling
Now it may seem odd to have a leveling section here, but leveling will probably make up the first 250+ hours of your game time (average /played is about 10.5 days to 60 even among private server players who have probably leveled 5 toons to 60 by now) so it's important to keep this in mind when leveling. First off before you even hit level 10: GET A BANK ALT. I made that stand out to really emphasize it's importance. Bag space is very limited in vanilla and you will need a bank alt if you really want to make the most money because otherwise you're gonna be deleting greys for quest items. every time you walk by a mailbox, vendor your greys and mail pretty much everything else to your bank alt. Also try to ah pretty much anything you can. Mystery meat, raptor flesh, or star ruby, I don't care trust me theres a million recipes in vanilla and generally everything will sell. Secondly, pre-60 just take skinning + mining/herbalism, it really doesn't matter which and mine/skin anything you can.
Farming
Everyone starts at 0 in vanilla (unless there is wow tokens) so you're gonna need some starting capital/something to do at 60. Disclaimer, while private servers do their best to mirror vanilla these values change quite a bit between servers so its unknown how each of the farms will do, and the values are kinda arbitrary, though its pretty much agreed upon DM North tribute runs are probably the best farming method.
- DM North Tribute runs (Hunter): 100-120+g/hour
- DM East farming (Mage): 50-80g/hour
- Mauradon Princess runs (Hunter): 50+g/hour
- BRD farming (Mage): 50+g/hour (though this may not work in vanilla)
- Bonus: Shatterspear troll farming (mage only and its exclusive to alliance) is 80-100g/hour and also allows you to afk level alts, but the location is out of bounds so it is likely you couldn't farm there in classic.
Flips and Trade/World chat
One of my most consistent money makers in vanilla was buying items cheaply from people in world chat and putting it on the ah. When someone says something like "WTS " just whisper them and ask the price and compare it to the price on the ah. I've made easy 50+g flips because people wanted to sell their items quickly and didn't want to wait for it to sell on the ah. Some good items/mats to look to flip are the devilsaur set (its bis for every physical damage class), devilsaur leather, arcanite bars (used for many high level blacksmithing recipes), twink items (you can find lists online), arcane crystals, elemental fire/anything for fire resistance consumables (especially early on in the server), and of course raid boes.
Professions
Professions are a bit weird in vanilla. I'd say in general most professions don't make you a whole lot of gold outside of certain specific ways they make gold.
- Skinning: Farming Cuoio di Gigantosauro and pretty much everything else is vendor price
- Herbalism: Running Fiore di Loto Nero routes at 60
- Mining: Doing diremaul east farms (miner + healer) for rich thorium veins/Cristallo Arcano
- Alchemy: The main money makers are transmuting Lingotto d'Arcanite, crafting high level flasks, and transmuting cheap essences to more expensive essences.
- Enchanting: Offering high level enchants for peoples gear, and disenchanting bop gear in some cases (enchanting is probably the most consistent money maker)
- Engineering: Doesn't make any gold
- Blacksmithing: One of the best ways is offering very specific late game crafting recipes like Elmo Cuor di Leone which are great money makers if you can be one of the like 3 people on the server lucky enough to have it (its really rare)
- Tailoring: can make some money on your Telaluna cooldown, but selling bags with cheap mats is about as good as it gets. Alot of your best craftable gear is bop so tailoring isnt insane for gold making.
- Leatherworking: Doesn't really make a whole lot but crafting items like the devilsaur set and hide of the wild often makes you some profit.
- Fishing: Farming raid consumables/deviate fish in barrens, honestly fishing is crazy gold/hour if you can stomach it.
TL;DR: Go hunter, farm diremaul north/mauradon, try to get in on the devilsaur mafia/devilsaur farm, monitor trade chat for good deals.