If you are only able to grab one Persona title in your lifetime, then make Persona 4 Golden that title.
It offers a great simulation experience, and its RPG mechanics are revolutionary and top notch.
The social interaction with characters are addictive, humorous, and very engaging, and all these are presented to players through beautifully drawn and rendered scenes and animations.
Persona 4 was arguably the best title in the franchise, but Persona 4 Golden was able to take that title away from its big brother simply due to the number of enhancements that it has made along the way.
If you do not own a Vita, then make Persona 4 Golden your number one reason and inspiration for getting one.