I highly recommend actually staying in the 20-60 range zones until you ding 62. The reason for this is that despite getting a slight penalty in experience for being over-level, the advantage of having flight will more than offset this. That, and WOTLK and TBC zones are the slowest part of the leveling process. Minimizing your time there as much as possible is worthwhile.
Make sure you have the two Flight-Path toys purchased, as this can save you time. It won't have EVERY flight path, but will have major locations for faster travel if you need to switch zones entirely(which you will). If you buy the toys on one faction, it unlocks for the other faction as well. So don't spend double the gold! These toys can be found at the heirloom vendor(Undercity for Horde, Ironforge for Alliance)
I am currently working full time on my Vanilla WoW leveling guides. Soon there will be a 1-60 speed leveling guide for Alliance, along with in-game guide versions available for my members area. As of right now, there is no members area, but if you would like to show support for my efforts into this project, you can simply donate to me via Patreon if you like (you will get some cool rewards in return). Or you can donate directly with PayPal if you like. All donations are highly appreciated and they will only motivate me more to continue making the best vanilla WoW leveling guides on the web.
Potions serve more utilitarian purposes, and it's up to you to decide whether to make use of them. The most common is the Swiftness Potion, which can provide you a handy boost in speed while going after annoying quest objectives indoors. These are generally MASSIVELY overpriced, because people know how useful they are. I opted not to spend the gold since Warriors are already fairly mobile, but slower classes may benefit greatly from these.
Class abilities were reworked dramatically across the board, with some still needing a serious balance pass. That left many players not only feeling underpowered, but having to learn how to play their characters all over again. Bosses in large-group raid dungeons that were easily killed each week by experienced guilds of players suddenly became challenging again, or worse, completely unkillable, halting forward momentum on old content for a good chunk of the high-end player base.
There are also a number of different online tools you can use to make yourself a better World of Warcraft player—and to help you decide what to focus on. Wowhead has a great Attunement Tool that shows you how close you are to unlocking significant milestones in the game, like unlocking new allied races, earning reputations with key factions (which will ultimately help you unlock faster mount speed and other goodies in the game’s expansion), and how far along you are in your dungeons and raids.
Dugi’s leveling guide is the leveling addon I’ve always used to level as fast as possible. It will show you where to go and what to do in-game, speeding up the leveling process. This is optional though, as the game already does a pretty good job at showing you where to go at all times. The addon does, however, come with a couple of other nice features and perks.