There are a couple linkshells that are for new & returning players. I know Shadowsong runs one, but I can't remember the other off the top of my head.
Which city did you start in?
FFXI-Garuda 2003-2009; Lakshmi 2011-8/20/13 (retired)
FFXIV: ARR - Ghost Bear, Balmung server
Free Company: BadAsp Super Friends <BASF>