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.
This gold making advice is applicable to most players, except if you are an enchanter, in which case there is a very strong case to turn them into dust and essence for your profession needs. As an advanced tip, you can explore the use of mobile apps that let you post on the auction house at the right time because the price of greens tends to fluctuate rapidly, and could mean a large loss of potential gold income.
For future reference, it is a great option to purchase mounts and pets as a long-term investment. Not only do their prices scale well even when a new expansion drops, but there is always a demand for them. The only drawback to this strategy is you would need a hefty amount of initial wow gold investment and also maybe have to go through the motions of spending for a guild bank.
Take breaks. Unless you're straight up no-lifing it over a weekend or something, this leveling process is going to take ~40 hours. But any time you do need to step away, log out. That tiny little bit of rested exp is insignificant...but you never know when something might come up and you'll have to leave for a longer period of time than you expected. Better to be logged out and safe(especially with War Mode on) than AFK waiting for a d/c. Plus, you'll need to stretch, eat, shower, and maybe sleep. XD
My second least-favorite part: leveling ranges. Zones are divided into leveling ranges; some are for levels 10-60, others for levels 58-80, and so on. On the surface, that appears to make sense; while there are odd moments where you're presented with the content from two expansions at once, it does mean that you're more or less going through content in order, at least by expansion if not by level.
Congratulations on reaching Level 120! There are a myriad of new things to do. The first thing you should do is head to your faction hub ship where you have been doing your mission table quests and footholds to pick up and complete the quests necessary to unlock World Quests. World Quests will provide you an opportunity to grind reputation levels, acquire gear, and gather Azerite. There are tons of new things to do that we will cover in our Level 120 Battle Guide found here: Level 120 Battle Guide