There are a multitude of new mages every day on the forums asking the same sorts of questions, so I'd like to take a moment to answer the most common ones here.
Is a mage for me?
Do you like blowing stuff up? Do you like having a bejeezus ton of ranged and point blank snares? Do you like relying on powerful direct damage casts? Do you like having a multitude of options available to you? Do you like having a small margin of error? Then mage is for you!
A lot of rather bitter people will simply say "LOL ROLL WARLOCK". I think that's silly. The mage class has a lot to offer, and I very often hear of warlocks turning to mages because they're "more fun".
Mages are extremely dynamic compared to most other classes. All our damage is direct, which means we need to do something every global cooldown in order to continue dealing damage. We don't have autoshoot or autoattack or DoTs to rely on.
We also have a small margin for error. We tend to be fragile if caught without escape options, so knowing when to use those escape options is crucial. While the margin for error is small, when we do things correctly we are VERY powerful, and victory tastes all the sweeter.
Mage fragility is a bit misleading as well. As frost, if you get a fair amount of health, you will be extremely difficult to kill. We are "slippery" against melee, and ice block and ice barrier provide a tough defense to break through for casters. Counterspell is one of the most feared interrupts in the game.
If this sounds like what you're looking for, then go for it! We are a fun and powerful class for sure.
What race should I be?
The general rule of thumb is Gnome for Alliance and Undead for Horde.
Gnomes get Escape Artist, which is an amazing ability against other mages (no shatter in novas) and against melees/hunters that are being particularly troublesome.
Undead get Will of the Forsaken, one of the best racials in the game for PvP that will drive priests and warlocks wild. Since shadow priests and warlocks can be two of the more difficult fights for a mage, this is a great tool for your arsenal. Combine with the PvP trinket and Ice Block and you become essentially unfearable.
Humans and Draenei tend more towards PvE. Perception is nice, but if we know a rogue is around it's often possible to AoE them out of stealth anyway, and barring the most skilled of rogues they're not really the toughest matchup for us. Draenei get a heal, which is nice, but compared to Escape Artist it's generally better to not take damage in the first place.
Trolls get Berserking, which can be useful, but generally won't be as game breaking as WotF can be. Blood Elves get an AoE silence, which is great for melee classes, but not as useful for a mage. The ability takes up a global cooldown, and since we're not dealing damage unless we're casting, it basically just stalls things at best.
That being said, racials won't make or break you. If you log on every day and say "Wow I want to gouge my eyes out because I hate gnomes/undead", it's absolutely not worth it. Play what you like most, and if you're undecided, then take the advice above.
What's a good leveling spec?
I generally answer this with the following.
Go fire to start. In the 30s or 40s or so, if you're bored of fire, try frost. From there on, both specs will do fine.
I was mostly fire when I levelled, with occasional dips into frost. Both specs are fine as long as you focus on one tree and focus on damage.
Don't split trees early on. Mage trees tend to be "top heavy", and the more you invest in one tree the more synergy becomes apparent. For example, Frostbite is nice, but if you get Frostbite and Shatter it's much nicer. Cold Snap is nice too, but it gets nicer with Ice Block, Ice Barrier, and the Water Elemental. Ignite is great, but it gets better with Critical Mass, Pyromaniac, etc.
Don't worry about 70 builds either. Most 70 builds only work because they have all the talents they do, and trying to build into them will make them seem weak until you actually hit 70. Don't worry about them until you're actually able to spec them.
I'd also recommend avoiding Arcane until later. The bottom of the tree is mostly worthless compared to frost or fire, and you don't really have a "go to" nuke to kill things with efficiently.
For specific talents, just focus on anything that increases damage or lets you deal it more efficiently. For example, Master of Elements is an awesome levelling talent, especially when combined with crit talents.
I should also mention AoE grinding, but as I did very little of it myself, I can't comment on it much. It's VERY risky on a PvP server, so if you're on one you should probably just stick to normal grinding. If you do want to give it a try, wait until you can get Improved Blizzard and Permafrost (do NOT get Frostbite!), then basically find a bunch of melee mobs and AoE kite them with your Improved Blizzard. Great xp if you can do it right.
What should I focus on for gear?
For levelling, +damage gear is amazing. Anything "of ____ wrath" works fine. The reason for this is that +damage allows you to kill things faster and use less mana while doing so. Using less mana means you have less downtime to drink, and killing stuff faster means you get more xp. It's a win/win really.
Anything else I should know?
There's a new mage FAQ on the mage forums located here that you may find useful. Hopefully this answered some basic questions for you though!