So I recently got Persona 5 and I'm absolutely loving it. I'm just starting the 5th Palace and if the quality of the game is sustained to the end, P5 could very well end up being my all-time favorite game. So, once I'm done with Persona 5, I want to work my way back in the series and play 3 and 4. The PS4 is somehow my first ever console from Sony (went with Xbox 360 last gen and was too young to know any better in the 6th gen), so I don't have the hardware necessary to play other titles in the series.
Since I also want to play some other PS1 and PS2 classics in addition to enjoying some features of modern consoles, I've decided to narrow down what I buy to either a PS Vita or PS3. Is the portability of the Vita enough to outweigh the cost and the more limited selection of classic titles? The only game that I would absolutely want to play that isn't on Vita is Demon's Souls. I'd greatly appreciate any input you may have.
Note: I am aware that the PS Vita does not have PS2 Classics available on it.