I would start with VI instead of VII

VII or X are good starting points. Then you can move on to IX and VI. At least, that's what I'd do ;)

Thanks for the input everyone. I am interested in FFVII since it seems to be the one that most people are talking about. One question though: Should I just wait and experience it for the first time with the remake, or should I just play the version available on the PS Store?

That's exactly right. I recently finished XCX and I'm now really curious about other JRPGs. Is FF 12 only available on PS2 though? If so, that's a bit of a problem...

It depends if you prefer an action based combat system to a turn-based combat system and if you don't like the dated visuals very much ... 

Start with 7. That's the one I started at and since you have a PS4, you can get it there with trophy support.

I don't really mind visuals from that era too much (Ocarina of Time is still one of my favs ever). Which one is action based and which is turn based? I guess I prefer action based, but turn based can be alright, à la Pokémon right?

The remake will feature the action based combat system and the original is turn-based combat but it's a fair bit more complex than Pokemon ... 

Unfortunately, yes. However its probably going to get a PS4 remaster in the near future

It depends, but I would recomend VII as well. It's definitely not the best Final Fantasy, but it's friendly and somewhat easy.