Never played a Final Fantasy game, would IX be a good place to start? I also own Type 0 HD which I bought on Amazon sale but have not touched yet.
IX is a great place to start, as it embodies everything the creator of the series is best known for.
The presentation is also easier to swallow than 7's. But if the graphics are offputting, maybe start with X HD, which is a bit more linear but is basically FF for beginners. Or go oldschool and try FF4.
Type-0 is not representative of the series at all, it's a spinoff. I personally enjoyed it despite its flaws but if you don't know shared elements of the series a lot of its references will fall flat, and it's an ARPG rather than a turn based entry like the majority of mainline FF's.
But 9 will teach you the pantheon of FF summons, what named series weapons are considered "ultimate weapons", what certain series classes/jobs are represented by which characters, names of spells, types of monsters, an appreciation of airships, chocobos, you name it, it's got it.