What the poster just described to you is Persona 4: The Golden which is only available on the vita which is an enhanced port with a moderate amount of new content but if you have a PS2 (which is unlikely judging from your account on platform ownership history) then you can play the original Persona 4 along with Persona 3 and it's enhanced rerelease Persona 3: FES. 

Persona 5 is indeed coming to both the PS3 and PS4. 

You don't need to play the other games to understand their respective stories in each game. It will help on understanding the background but it isn't necessary just like Final Fantasy ...

If you want to start out that badly then get a PS2 and start with Persona 3: FES cause Persona 1 and 2 are outdated as hell ...

You can actually play Persona 1, 2, 3 Portable and 4 Golden on Vita. It's just that Personal 4: The Golden is the only physical release.

Oh. Well then that wouldn't help.

I think I'll wait for one of them to be released on PS4 PSN or PS Now

You can't exactly play Persona 3: FES though since that's the definitive release ...

I can see you're a bit confused SOR, so allow me to give you a run down of everything you need to know

But Persona 4 isn't a patch on Persona 4: The Golden, so it's a trade off either way.

PS Now is only meant to stream PS3 games but with the release of Persona 3: FES on PSN it's possible that you can play that on your PS4 once it's available on PS Now ... 

Sony is normally pretty good when it comes to releasing older games so I'm confident that I'll be able to play one of them eventually. They will release PS / PS2 games on PS4 either through PSN store or PS Now I'd think.

True but I highly doubt the OP is interested enough in the Vita to get the definitive P4 experience so hopefully Atlus will be as kind as to port P4G to the PS4 ...