In order from best to worst (for dungeons)…
Tank:
Feral Druid - Best choice. Least gear dependent. Best AoE DPS/Threat, and best single target DPS (but not threat; Sunder Armor OP). Very good for soloing when not with your group. Can also DPS with the same gear, or heal with another set of +Healing gear. Unfortunately, you’ll probably have to respec to Restoration once you start raiding, as few raid groups will have use for a Feral Druid until AQ.
Fury Warrior - More DPS than Prot. Protection talents not really useful until raiding. No debuff limitations in a 5-man, so Deep Wounds helps with threat. Better for soloing that Protection. Very gear dependent.
Protection Paladin - Pretty garbage. No taunt. Really good DPS/threat against Undead, otherwise pretty bad. Gear forces you to choose between mana or Defense, both of which are necessary for Paladins to tank, so you’ll always be lacking something.
Healer:
Shadow Priest - Yes, Shadow. Holy talents offer little extra healing, but much less damage. Can solo, and has more efficient damaging spells for boss fights. Lower cooldown on CC, and extra spell: Silence. Can still cast Resurrect. You might get into a raid group as Shadow, but you’ll probably have to respec to Holy at 60.
Protection Paladin/Enhancement Shaman - Depends on faction, but both serve the same function. These will be the specs you level solo in. Can heal just fine with a set of +Healing gear. Decent heals, great buffs. You’ll have to respec to Holy or Restoration once you start raiding, though. Several needed in raids.
Some Horde groups bring Enhancement Shamans equipped with Nightfall to maintain high up-time on the debuff, so you might get to stay Enhancement.
Feral Druid - Same as Shadow Priest, basically, except you don’t get an extra CC, Silence, and you can’t cast Resurrection.
DPS:
Warlock - Oddly one of the most useful and most powerful DPS classes, yet one of the least populated. Can summon. Has a pet for off-tanking. Can CC. Soulstone. Basically totally self-sufficient; no need for heals. Great soloing. Lots of Warlocks needed in raids.
Mage - Great DPS. CC. Vending machine. Portals. Decent soloing. Lots of Mages needed in raids.
Rogue - Consistent DPS. Fairly weak CC, but lots of it. REALLY rough time soloing, though, so only pick this if you plan to mostly be in groups. There will be TONS of rogues, so it might be hard to find a spot in a raid.
Fury Warrior - Always use two-handers while leveling. You don’t have the +Hit gear to dual wield yet. Great DPS with gear, but arguably the absolutely worst solo leveling experience of any class and spec, and utter trash without gear.
Hunter - Pretty bad DPS, even though they’re a pure DPS class. Decent CC and kiting. Best soloing by a long shot (pun intended). Pet can off-tank. Multiple pets means multiple roles, so great utility. Can provide a unique buff with certain pets. Can run out of arrows, so prepare for your Hunter to say they need to go buy more, or start meleeing. EVERYTHING is a melee weapon, so prepare for the Hunter greed.
Anything Else - The rest are all equally pretty bad.
Just so the OP doesn’t get confused, and no offense to you, but this is silly. In vanilla, you wear the best gear for its stats, regardless of its armor type. Hunters didn’t exclusively use Mail, and in fact don’t use Mail at all until 40. Even then, lots of Leather gear, especially when leveling, is BiS.
This is true for every class, not just Hunters. Expect your healers, even Paladins, to roll need on Cloth gear if it has +Healing. Expect your melee DPS to roll on Leather because all Leather gear is seemingly over-budgeted with +Hit, +Crit, and Attack Power.