I play on Odin

Most of the well-known Linkshells and top-tier players that I am aware of are on Odin, Asura, and Quetzalcoatl. I've become friends with several of them, and from my experience, they are all very willing to give great advice and answer questions if you're nice to them. They are all really great at the jobs they play, so perhaps your server choice could depend on what you want to do.

Llewelyn is in my social LS on Odin and also has a very good Event LS with many good players. If you like soloing, Mischief is also on Odin, and he has accomplished many very impressive solos with Scholar and Blue Mage! (Youtube: Mischief17).

I'm sure Asura has many very notable players and LSes, but I've never played on Asura. If you like Blue Mage, I think Spicyryan is on Asura. Extremely knowledgeable Blue Mage player, and has lots of guides and videos as well.

If you like playing pet jobs, there is a very well known Pet LS on Quetzalcoatl called BzerozerotyPirates, and I believe they are pretty inclusive to pet job enthusiasts. They are very good too. Falkirk and Beaztmaster are both very good Beastmasters, and Trulusia is an excellent Puppetmaster (Youtube: lethalfalcon08, Tr3s1no). I believe Quetzalcoatl has a smaller population than Odin and Asura though.