If what you want to do is cast from afar "dot-n-run pattern", than you are already on the right track. I would go with a lock.
If this is your mindset I would guess you would also be interested in rogue, because you can do similar hit and run tactics as a twink. Lock down the clothies and then sprint away. Overall any and every class can be turned into a fun level 60 twink, it just depends on what you want to do.
This question gets a bit tricky to answer... Starting from scratch, if you buy just vanilla WoW, you can experience the original world as it has been destroyed by the Cataclysm expansion. You can level up to level 60, but cannot access professions, areas, races, or other such things from any of the other expansions.
In order to access Outland, jewelcrafting profession, and Draenei? / Blood Elf races and starting areas, and level 61-70, you will need vanilla WoW + the Burning Crusade expansion.
In order to access Northrend, Inscription profession, and Death Knight class, and level 71-80, you will need vanilla Wow, Burning Crusade expansion, and Wrath of the Lich King expansion. Oh, and a prior level 55+ character on your account to play as a Death Knight.
In order to access the misc Cataclysm level 80+ areas, Archeology secondary profession, Worgen / Goblin races, and level 81-85, you will need vanilla WoW, Burning Crusade expanion, Wrath of the Lich King expansion, and the Cataclysm expansion.
Those are the restrictions. You can play on whatever realm you want with whoever you wish. You just may not be able to reach all the areas they can.
You can trial every bit of it with the 10 day trial, though I don't quite know how they treat it when your time is up.
Best Answer
The "Free to Play" bit is only for trial accounts. Accounts that have previously been full accounts will need to be resubscribed, and can not be played for free up to level 20.