Now I'm curious, because I've yet to find one way or another what people have designated as the unofficial servers. Still trying to find the RP one.
http://ffxiv-roleplayers.com/Gilgamesh and Balmung are the unofficial RP servers for NA/EU and I think Masamune was the unofficial RP server for JP.
As far as server population goes, both Balmung and Gilgamesh were packed to maximum capacity during open beta, its a possibility that there could be a wait or restriction on creation of new characters regardless of which you choose.
I was originally planning to be on Gilgamesh myself but it was an unpleasant experience in phase 3 and 4. In addition to being the highest population, it is also server of choice for many other communities that don't take kindly to RP or each other- I would liken it to a combination of the Moon Guard, Proudmoore and Illidan servers in WoW.
The alternative, Balmung is quieter but it is a legacy server so there are some people that like to show off and wave their e-peen around but overall, I haven't had that bad of an experience so far (my only issue was legacy jerks on Goobbue mounts blocking NPCs)
I couldn't get into Masamune during open beta but in addition to RP I think it was also the unofficial international server.