When you sign up for WoW, you create an account (username, password and profile as usual). This account is not yet a WoW character, it's just Blizzard's introduction to RL-you. You may have up to fifty characters per account, with a maximum of ten per server.
The first question when creating a character is "on which server?" (This section is dull but of great significance.) Unlike SL which is one single contiguous world, there are hundreds of duplicate WoWs, and you can only interact with avatars who are on the same server as you. The practical consequence of this is that if you wish to join WoW to play with friends who are already there, you must find out the name of their server. (My Alliance characters are on "Kul Tiras EU," for example.) But there's a catch: the "EU" in the servername stands for Europe, and you won't be able to sign up there unless you entered the Internet from a European IP address. (To be clear, this applies only to creating characters, I was able to play on my European servers while in New York.)
A further complication, or enrichment, is that Alliance and Horde cannot communicate with each other. Your Hordie rogue cannot betray her comrades by sending their battle plans to your Alliance paladin (and that example is, of course, exactly why Blizzard enforces this restriction). Guilds too are faction-specific: either Alliance or Horde. Given, therefore, that your Allies and Hordies will be separated anyway, you should take advantage of this to create them on two different servers to have the maximum number of avatars available to each: my Allies are all on Kul Tiras EU, my Hordies on Arathor EU.
If you are joining friends, then clearly you choose their server, otherwise have a look at Warcraft Realms' information about the US or EU servers. What you should look at is first the language (if EU), secondly whether PvE or PvP, and thirdly the number of avatars in your chosen faction: if you are picking a server for your Horde characters, then choose one which has a largeish number of Hordies already registered. You need at least six thousand characters in your faction
Having got this far, you now face more interesting choices: your faction, race and class. If you are joining friends, then you'll need to be the same faction as them, otherwise you'll find that one faction appeals to you more strongly than the other. Go with that feeling. For example, I'm a natural-born Allie, even when playing a Horde character I feel like a double-agent spying for the Alliance.
Races (human, tauren, orc, night elf etc) are faction-specific, e.g. if you want to be a goblin then you have to be Horde. As a beginner, there is no particular reason to choose one race over another (other than to be in the right faction and class, see below) so choose an appearance that appeals to you. (Speaking of appearance, visitors from SL will be disappointed by the paucity of choice. You can change the style and colour of your hair later on in the game, but your name, gender, skin tone, facial shape and ears are fixed permanently at this stage.)
Classes (hunter, priest, mage, warrior etc) are race-specific: e.g. if you want to be a druid, then your choices are worgen or night elf (Alliance) or tauren or troll (Horde). This is probably the most significant choice you'll make, as the class of your character determines what xie can do and how the rest of the world will interact with hem. Let me take this opportunity to introduce the WoW Wikipedia and in particular its fulsome and excellent Newbie Guides. I strongly recommend that you read the Character creation guide at this point.
That'll do for now. If you have any questions, feel free to mail me at wol dot euler at yahoo dot de.
* Updated: dungeon teams are one of two exceptions to the rule that you can only talk to characters on your own server. They appear to be drawn from all servers in your language and domain (EU or US).
** Updated again: realm size alone doesn't guarantee a good economy. There are currently 6930 Hordies registered on Arathor, and its auction house is sluggish; but the 5709 Allies on Kul Tiras support a thriving AH. It's a mystery.