There are a few things to keep in mind when you pick a server to play on.
Where are Your Friends Playing?
With each character your create, you can only interact fully with people on the same server (realm) and faction (Horde vs Alliance) as your character. You can create characters on different servers if you like, but then they cannot support each other by e.g. swapping gear, money, supplies or mailing items to each other, etc.
You are allowed limited access to other servers. There is, however, the possibility of paid transfers. For a fee, you may move one character to another server. The character will be unplayable while the transfer occurs, and a character can only be moved once every month. That is to say, if Alice was moved, she cannot be moved again for a month, but your second character (“alt”), Bob, can.

Other than that, the only way for people on different servers to meet is through the cross-realm PVP battlegrounds, where characters from servers in the same battlegroup can meet. However, there is no guarantee that two players who would like to interact will be put into the same battleground game. In addition, cross-realm instance grouping is possible within a battlegroup. Cross-realm, cross-faction, and cross-game chat is now live in Battle.net games as of Patch 3.3.5.
What’s Your Time Zone?
Playing on a server with a time zone similar to the one you live in means more people will be on around the time you’re going to play — assuming you play during peak hours, which varies but is usually between 6 p.m. and 10 p.m. on the server during weekdays. This affects the game in several ways, some of which might not be immediately apparent or affect you until you reach higher levels.
Your realm’s time zone can affect your World of Warcraft experience in following ways, among others:

The number of people who are available for you to group with. This is critical for instanced dungeons, and if you are interested in endgame you may find that this is your most important consideration as you will want to be active around the same time that the people in your guild are raiding.
The amount of buying and selling that is going on and the prices in the auction house at peak hours.
The amount of competition for resources that are out in the wild. The more people playing, the more might be looking for the same herb or quest mob that you’re looking for.
The number of opposite faction players who are around to attack you (especially if you are playing on a PVP server).
The amount of activity going on in Battlegrounds.
People who are usually unable to play during peak hours often try to play on a realm in a different time zone than the one they live in. If you tend to be available earlier than peak hours, you might want to look for a server that is in a time zone earlier than where you live. Similarly, if you tend to be available later than peak hours, you might want to look for a realm that is in a time zone later than where you live. This will generally maximize the number of people who are around when you are also looking to play.
Which Language Do You Prefer to Speak In?
The European Realms are divided up by which language is primarily spoken on them. No rules exist that ban you from speaking other languages on the servers, but you may feel more comfortable on a server where the majority of players speak a language that you understand.
What’s the Server Population?
Each realm has a population listed on the server selection screen. Each realm is characterized as having Recommended, Low, Medium, High, and Full population. Recommended servers are what Blizzard thinks will give a new player the best experience, while the rest are categorized based on how many players are currently logged into the realm. These servers change throughout the day, so you may want to decide on a server at the time you would normally play, so that you’ll know how full it is normally. You cannot create a character on a Full server unless you already have characters there. Some High population servers have wait queues during peak hours. This means you cannot sign in at all to them until other people have completely logged off of that server.
Each type of realm has benefits and drawbacks for new players.

Realms that are usually at “Low” population are often very welcoming of new players. The lower population means that there is a great deal of demand for new players on the realm, and experienced players will often be more willing and helpful in bringing a newer player up to speed than on other realms and may have more patience with new players in general. However, the realm’s Auction House will probably not have a very wide selection of items available to buy and it may be challenging to find players to group with. There will probably never be a need to wait in queue to log into these realms.
Realms that are usually at “Medium” populations offer a compromise between extremes. Not much, if any demand, exists on these realms for new players, although they are usually not disliked either. These realms usually have a wide variety of items on their Auction House and finding other players to group with will not usually be a problem. Even at peak hours there is seldom if ever a queue to log into these servers.
Realms that are usually at “High” populations can be rather discouraging of newer players (and not just those who are inexperienced with World of Warcraft). These realms sometimes have queue times to log in that can range from a few minutes to an hour or more. While the Auction House is often full of items and there are usually a lot of other players looking for people to group with, be in mind that with a larger group of people there are can often be a corresponding increase the number of players who behave badly toward others or are outright unpleasant to deal with, something that on Low and Medium population realms are at a relative minimum (though hardly non-existent). On a High-population server, a player looking to act negatively toward other players will probably be able to find other like-minded individuals, and even find entire guilds devoted to this sort of behavior.
Realms that are often at “Full” populations are much like realms at “High” populations, but even more so. Players on these realms may be outright hostile to new players regardless of their experience with World of Warcraft, as login queues on these realms may regularly last hours. However, if you are able to log in, the Auction House will be full of items and there will be a vast number of players who you may be able to group with. 

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