One thing I noticed during my first couple of weeks playing is that, compared to FFXI, you really don't party very much. During my time in FFXI (though I quit some 6 years ago), I met a lot of people in game and made a lot of friends in game. It was very social, and even at lower levels or just starting out, it was common to spend more than half of your first two weeks playing in parties.
In FFXIV, the social aspect which I enjoyed so much only really started the past couple of days since I joined an FC. Even in fate burn parties, there isn't much chit chat the way I remember there being in a lot of FFXI exp parties. This social aspect is not only, imho, a very enjoyable part of playing an mmo game, but is also critical to advancement in the game without hassle, to getting to know crafters and gatherers with skills compatible with yours, etc.
So I my advice to new players would be to find an FC soon after getting started. Be wary of anything that seems ill-advised, like those FCs which send random spam invites. Talk to some people with FC banners after their names. Do dungeon runs more than once, they're your best bet for being able to meet and evaluate other players. Find some good people and get together. You'll be glad you did!