That being said, if you have any chance of enjoying this, then I recommend you;
1. play persona 4 and if you have a vita, the golden version.
2. watch the original anime (http://myanimelist.net/anime/10588/Persona_4_The_Animation)
I love the characters in Persona 4 and overall I think they did a solid job on both animes. Unlike a majority of the P4 fans, I feel like this anime did honor to the game's story. So I'll try and keep this as simple as I can. Why did I like this anime and the original that its based off of?
1. I feel in love with the characters and world of P4 and the shows did justice in bringing so much of what I liked about the characters back from the game and even stepping it up a notch. If you are new to P4, then welcome to a well rounded crew of characters that mixes anime mystery and slice of life with Scobby Doo adventure and antics, no I'm not kidding.
2. Since the games main character Yu is a Silent Protagonist, its great to see his character be given so much life in the animes. Everything that made him badass based off the players choices, are personified (hehe) in the show. Scenes like the P3 nightclub are made that much greater or in the case of this anime, the Christmas and beach events.
3. This is where most people will disagree with me and why I encourage you to watch the original anime first. Yes the main story is almost completely lacking in this anime, and I'm Glad it is! Why? Well while I understand not everyone fits in this group, its overkill for me. I played the original game to completion, I also 100% the golden version. I also watched the original anime before this one. While I love the story, I also am tired of it as well. I played through the game again and that was fine, but the last thing I want to do is rewatch all of it AGAIN just to see some of the "extra new stuff". This anime gives you Marie's story and all of the awesome extras that the golden game added without you having to rewatch the same stuff again.
The creators made this anime catering to the fans who watched the original already. A similar thing is done in Full Metal Alchemist Brotherhood. They rush through the things that sync up with the original anime and when it branches away, they start to give the anime a slower, more depth paced feel, (even if it was a roller coaster ride). The anime producers do this to prevent the original work they did from becoming obsolete while still appealing to the fans of that original work.
So all of that being said, watch this either after or alongside the original anime and you will find yourself in for an enjoyable time.
