Hunters & Mages usually are considered the very best gold farming classes in WoW classic, with Warlocks right behind.
I prefer hunters as my main became a hunter in vanilla WoW, however, it all depends on playstyle. GameMS offers a lot of cheap Classic WoW Gold, which is free for players to choose from.
Hunters are a strong solo class with having access to pets, powerful ranged damage and an awful lot of utility like feign death, which comes in handy when farming dungeons. Hunters may also be the fastest leveling class.
Hunters can solo many areas that other classes cannot like advanced level dungeons like Maraudon. If you don't have enough time to grow, you can choose to buy WOW Classic Boosting from the GameMS website.
Mages can also be a solid choice if you appreciate AoE farming. Mages may travel around quickly and save gold by summoning refreshments. And they may also sell food & drink for any extra gold.
Mages can AoE farm certain dungeons and open-world spots, causing them to very good for gold making also.