1.a) Check the population of realms:
You also don't want to be on a pathetically outnumbered faction (example, an Alliance with a ratio of 1 Alliance to 10 Horde) on a PVP server.
Don't put too much stock in the "low"/ "medium"/ high" indicators for realm selection in-game. These just indicate the number of players logged on at that time, not the actual population. They also seem to be inaccurate, as even some low-population realms perpetually display as "medium".
1.b) (US) Check the realm time zone:
2) Check the location of the data centers:
Note, however, that realm population size will affect your gameplay a lot more than the small difference in latency.
3) And finally, filter your choices according to your PVP, PVE, RP, Oceanic, Latin America, or similar language spoken (for EU) preferences.
Note: Sorry, Oceanic players. The data centers for Oceanic realms are still located in the US, and your ping will be pretty much the same as if you had rolled on a non-Oceanic US server. The only difference is that you will be on the same realm as a ton of other Oceanic players and be able to play when people are awake.
>>Optional, PVE-related<< (Ignore this if it confuses you)
A raid is an advanced form of dungeons, performed at max level by groups of 10 or 25 players.
This has to do with raid progression on each realm, and may matter to you when you get to max level. Some realms tend to breed raiding guilds that are more hardcore about progression than others, with the result that they will progress further in raids earlier than other realms.
4) Check the raid progression on the realm:
5) Check the type of raids and guilds on the realm:
Make sure it wasn't one outlier that's skewing the progression curve for that realm.
Fancy 25-man raids? See if there's a respectable number of 25m raiding guilds on that realm.
6) Check the official realm forums:
An active realm will have raiding guilds posting their recruitment needs there. You'll be able to get a feel for how active the raiding scene is and possibly also find a guild ahead of time.