Earning gold in World of Warcraft: Classic is all about optimizing your spendings. Back in the day, your character’s skills were acquired from a trainer, using money. Don’t just buy everything he or she offers! Read the skill descriptions and be mindful about them. Quite a few characters can live through the levelling process without learning some of their utility or damage spells. These won’t go anywhere and you’ll be able to learn them later on.
Mounts also take up space in your bags, bags which will of course be much smaller. Every bag space counts. With no guild banks, and much smaller storage space, your bank alts are going to be essential. You’ll need to remember to always post everything back to a bank alt, and to remember to get everything from the mail box to the Auction House. Which is only in Ironforge or Orgrimmar.
That's not to say that everyone has an unrealistic vision of what vanilla WoW was like. There were already plenty of people on the WoW Classic forums pointing out that perceived bugs are just recreations of the original game. And as noted before, a flaw to one player is a key component of the original positive experience to another. WoW Classic will surely please plenty of purists in spades. But this goes to show that it won't be for everyone who has fond memories of the game circa 2006.