Pick druid, paladin or monk. Get heirlooms if you can. Grind mobs until level 5 - 6. Start doing the easy "just kill these mobs outside town" quests until 15. Queue rdf as every role and do every dungeon you can (with heirlooms you could probably solo the dungeons) while you travel to higher lever zones. Keep doing the simplest quests while you're waiting for rdf (which shouldn't be long). I leveled a druid to 100 once doing this in maybe a day /played, but he was also rested for most of the process.
There are professions you can train in to make money in the game. You can be an herbalist to pick useful plants; an alchemist to make potions; a miner to mine ore; a blacksmith to craft armor; a jewelcrafter, who can cut gems that can be socketed into certain items to augment them; or an enchanter, who can enchant items to have bonus stats or effects.
Fully rested experience (this is the blue color your experience bar takes instead of purple) grants 200% more experience per kill. Quest experience does not work the same as mob experience. Instead of just using the rested bonus, quest experience pushes the bar further upwards extending the rested bonus. Say if half your experience bar is blue. If you turn in 10 quests all at one the normal experience from them all could boost a character a full level. Unlike mobs where the experience gain will use up said bonus - the quests merely 'push' the bar further. Doing this could net you a level and still have the 200% bonus for mob kills applying to milk the rest bonus.
At 98 you have the option to drop what you're doing and return to your capitol city to start the quest for your Legion Artifact weapon. However, I do not believe this is necessary to do right away unless you're struggling with kill speed in your current gear. I would recommend waiting for a natural pause, such as hearthing to repair and clear your bags. From 100 to 107 you won't even really fight mobs that often; only just enough to clear the way to any treasure you need to pick up.
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The reason for this is simple: Most players don’t need a lot of gold or care very much about it. An active player might earn an income of a few thousand gold per week from sending followers on missions and doing World Quests that award gold. They might then spend most of that money at the auction house buying things like flasks and stat-buffing food to do raids and Mythic+ dungeons. Gold just isn’t a big deal for them.
Drustvar is far and away the hardest Alliance zone, which is exactly why you want to do it first. If you have legendary items, they’ll still be usable, and if you don’t, this zone will still be easier early on than it will be later. Drustvar is also extremely fast and will let you jump out ahead of your competition in other zones, which means fewer players around to take your quest objectives.
Kael'thas - Alliance Kael'thas - Horde Karazhan - Alliance Karazhan - Horde Kargath - Alliance Kargath - Horde Kazzak - Alliance Kazzak - Horde Kel'Thuzad - Alliance Kel'Thuzad - Horde Khadgar - Alliance Khadgar - Horde Khaz Modan - Alliance Khaz Modan - Horde Khaz'goroth - Alliance Khaz'goroth - Horde Kil'jaeden - Alliance Kil'jaeden - Horde Kilrogg - Alliance Kilrogg - Horde Kirin Tor - Alliance Kirin Tor - Horde Kor'gall - Alliance Kor'gall - Horde Krag'jin - Alliance Krag'jin - Horde Krasus - Alliance Krasus - Horde Kul Tiras - Alliance Kul Tiras - Horde Kult der Verdammten - Al... Kult der Verdammten - Horde
Special mention is the Darkmoon Faire Top Hat and WHEE! buff. While not always available due to the DMF being inaccessible most of the month, if you happen to be leveling when the DMF is running, it might be worth your time to go and get these. AFAIK they do stack with heirlooms, although I have not personally tested it. Fair warning: These buffs do NOT stack with each other, and the hats disappear after the DMF goes away later in the month(unless you only log in when the faire is running).
Footholds into enemy territories can be done as you grow in levels and should be completed before reaching Level 120. Take the time after completing your first zone to do your first foothold. Similar to how your initial zone selection was largely irrelevant, this selection is, as well. Simply pick one and complete it to earn your Mission Table second champion. Send your champions out on missions, recruit troops, and then head back out to quest in your second zone selection.
As you're leveling, I generally recommend you just follow the natural flow of the progression through each zone. They're laid out fairly reasonably. But don't be afraid to hop around, especially if you're near a quest objective. You shouldn't actually need ALL of the zones listed to reach 62. Pick the ones you like best. It's much more important to simply be as focused as possible and flow from one quest to the next.