Depends on what you're looking for really. Are you looking for a PVP focused server, raiding, crafting? Or just a bit of everything to start out with?
According to the census, the most active realms in the US are Leviathan, Gilgamesh, Cactuar, and Balmung. With the least active being Goblin and Zalera, and everything else being squarely in the middle. However even the smallest servers do have fairly active communities, they're just more closed knit than others.
If you're wanting to see what the game has to offer in full, I'd try Leviathan or Gilgamesh first and then branch out from there. Balmung is very active, but we're primarily RP based with everything else thrown into the mix. We have active and fairly decent raiding FC's, but if RP isn't your preference you're better off trying another server.