Where to Start?

[Atoli]

I just started a new character in Limsa, and there are lots of things to do.
I got to rank 9 just by following the main storyline and doing some available miniquests in Limsa + only 2 leves.
No grinding either (although you can grind from lvl 1-10 in about 10-15 min if you want to..)

I still have mini quests to do, but I guess I'll do a few leves and behests now for Gil and Exp until lvl 12/13 when the main story continues.

Shposhae is a lot of fun and has lots of really useful equipment for any fight and magic class.
Maybe you both should find a LS first, it's way easier because they can help you, explain stuff and you also always have people available for group content like dungeons

So..no, you don't have to grind a few hours until you get content.
First content you get is the main story line which starts at rank 1.
Later on though, you WILL have to grind a bit or do leves/behests to get to the next rank at which you get more content.
That's not different from other games though in which you rank up through quests.
Having 500 quests all saying "kill 10-30 mobs of this type because I don't like them" is the same kind of grind as getting leves in FFXIV which tell you "kill 12 mobs of this kind because there are too many".