I do not recommend going for TBC, although I remember Hellfire peninsula to be decent, everything else is rather slow. Instead go for WotLK, Borean Thundra gets you levelled very fast, and then you can head straight for Icecrown at 67, which is also insanely fast, although admittedly has a few elite quests. You can go to Sholazar Basin alternatively. 2 zones should get you 60-80 no problem.
Heirloom experience should be boosted, now that zones scale. If a zone scales along with me, it shouldn't matter if it gives me 20 levels instead of 10. I'm still enjoying the experience, even as a veteran player. I don't need to see every zone on every character again; that's the point of heirlooms. I can still enjoy the leveling experience, and the scaling, and the full outdoor experience of the zones -- and still get to the end game content I enjoy in a somewhat reasonable time as an employed adult. And the change wouldn't affect new players.
Leveling from 58-80: Outland and Northrend Recommended leveling paths for level 60-80 players in WoW. Includes best zones in Outland and Northrend, as well as notable quests and rewards. Leveling from 80-90: Cataclysm and Mists of Pandaria Recommended leveling paths for level 80-90 players in WoW. Includes best zones in Cataclysm and Mists of Pandaria, as well as notable quests and rewards. Leveling from 100-110 in Legion How to level quickly in World of Warcraft Legion from 100 to 110. Includes heirlooms, assaults, useful items, and experience boosts. The Big Bag Guide This guide covers bags from drops, quests rewards, vendors, and professions. Additionally it also covers item type specific containers.