I'm more of a Kingdom Hearts fan than a Final Fantasy fan, but I dabbled in FF a little bit (VI and XII being my favorites) and XIV seemed to have a similar art direction like XII so I gave it a go.

Now I have a pile of FF games I've been slowly playing through since I never really cared about the franchise until I joined XIV! I personally think XIV is a pretty good first game to start with since it's accessible and the story is decent enough to get you interested in seeing the rest of the series.