Hi Alex and welcome to the game.

It's easy to feel overwhelmed but take the game at your own pace and you'll learn to love it. As noted previously the main thing to focus on is your Main Story Questline (MSQ) as this is vital to unlock everything FFXIV has to offer (plus the story is awesome and just gets better as you progress).

To add what's already been said here:

1. Twitch is another great place to meet other players and see the game in action (though just take note of what the streamer is doing before watching - there may be spoilers!). I personally love watching MoodyMoomba or ZeplaHQ - both great streamers who do quite different things but you can chat to other viewers who are in-game whilst watching too.
2. Attacking another player's enemy shouldn't cause you grief (especially if they seem to be struggling) - the only exception I would say is if the other player is a Blue Mage (BLU) as they learn their spells from the enemy mobs - if you kill it before they learn the spell they may be upset. If in doubt ask if they want some help.
3. Don't pay attention to players who look like they've headbutted the keyboard to choose their name - these are usually bots/gil sellers who may be trying to trick you into buying stuff with real money, or trying to gain access to steal your account. You can report these via the in-game help tool.
4. Don't be afraid to talk to other players - this is a really friendly community. When you start doing dungeons tell the party you are new/first time and 95% of the time you'll find the other players willing to help you with your rotation, offer tips about your job/gear and explain the boss mechanics to you.
5. Above all - have fun!