So it looks like Ultros, Leviathan, and Excalibur are the server names I've seen mentioned the most thus far with Ultros and Leviathan being the two preferences amongst the newbies or those starting fresh :)
I like large communities, but unfortunately I don't like the server they chose. We will all be playing the same game though, so we can still be a community on these forums.
Join Excalibur if you want to see tons of level 50 capped players running around with an awkward economy (since they will have so many items ready to spam sell.)
Join Leviathan if you want to start fresh at level 1 where people will be 20 max during Early Access. A lot of new players will be playing this server from what I can see.
Join Ultros if you want the above but want to be in a large linkshell. I preferably stay away from large guilds because I like to know each member instead of "oh hey fellow zam member!"