1) Hunter (beast master spec). Fast levelling, high damage, virtually no downtime, solo elites and group quests without a problem.
2) Warlock (affliction till Outlands, then demonology spec) Same as hunter - little downtime, elites and group quests handled with relative ease.
3) Druid (feral). High melee damage, swift travel forms, self-healing, can tank.
4) Paladin. High melee damage, self-heals, movement speed increases via talents.
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The rest
Edit to answer your question: you can change your spec any time you like, as long as you have the gold to pay for it. The first time you do it it costs 1 gold, then each time it gets more expensive until a maximum of 50 gold. Later in the game when you've amassed 1000 gold you can buy dual-spec, meaning you can switch between two different specs without having to pay a trainer.
