It's really only 3 dungeons through 40, I haven't decided horde or alliance yet, but if horde I'll do RFC at 13, WC at 16, SM at 25 - for alliance DM at 15, Stockades at 22, SM at 28. SM will take me through to 40 and I would stay there farming exp/gold until I could afford my mounts and skills I want. From this point it will depend on what level I am, do Uldaman for a few levels then ZF at 46, then BRD at 52. That will put me to the level 60 dungeons, so I can start doing LBRS (for the key) or keep doing BRD if there are drops later in the dungeon I want.
Since I'll have at least 1 mage and 1 warlock on my team, I'll be able to hearth/port to town to vendor and buy skills. As well, I will have 1 enchanter and 1 tailor, so I can DE and make bags to help extend my time in the dungeon - even though using DE will make me farm later for my mount most likely.
This is purely based on my memory (from 15 years ago) and wowhead level ranges for the dungeons. I know I'll be skipping any class quests that aren't beneficial for my team leveling, so I'll only do the level 10 class quests and then skip basically all the other ones (so no voidwalker, no zerk stance, stuff like that), just because I feel they would be a waste of time to do while leveling and I can just do them once I get my mount - so I may go back at 40 and do some of them.
This is also assuming I level my 5 box team first, I am still undecided if I'll 5 box first of if I'll level a solo character first then boost a team with that character.