I'm not one for RPGs but the products Atlus release have a special place in my heart. This one especially.
Persona 3 is a game that's pretty difficult to summarise but basically it can be summed up as:
High school students battle evil monsters in an hour between midnight and 1AM by shooting themselves in the head and summoning creatures from a variety of mythos. And by day you live a normal life or try to.
The "normal life" part basically features a game mechanic known as Social Links where you meet new characters and form bonds with them allowing said creatures to get stronger depending on how close you are. The characters you can meet range from your classmates, a shay salesman, a mmorpg player or an elderly couple. All of the Social Links are interesting and more than a few of them tug at the heartstrings. Just play through the Sun Social Link for proof of that.
In terms of gameplay I admit I'm not too familiar with turn based RPGs aside from Pokemon but it pretty much works the same but sometimes it's less obvious what effects what or what type of spell your actually using. Thankfully, you adapt pretty quickly. Some spells range from lowering or increasing stats like attack and defence or poisoning enemies or using elements to figure out weakness. ( Pro tip do not think stat spells are useless or the game will punish you for it later on)
The plot follows a similar wonderful mess to other Atlus games. Things start of simply enough then the plot thickens a bit and then there's the big shocker which reveals that everything the character's have done so far is doing more harm than good wonderful mess et cetera. I know I'm taking the mickey but in truth the plot is pretty good and well worth shifting through. That being said there are times when the action takes a back seat to something that barely qualifies as relevant and the last few days in game time will be nothing but Social Link related. One other game mechanic worth mentioning are the Fusion Spells in Persona 2 they required your party to have certain monsters with certain attacks and certain turns. In the original Persona 3 all you needed was the two Persona and you could use the spell, here you need certain gems and jewels to give to some woman in town and if you have the right amount you have the fusion spell, which you can only use once and it's normally not worth the effort mainly cause a lot of Personas have attacks that actually work better.
There are two stories a male and female. Gender aside the difference is pretty much Social Link related either dropping Social Links, editing them or adding new ones.
Finally there is Persona Fusion system. Fusing Personas allow you unlock new Personas this is where Social Links really play their part as the better a Social Link the more powerful the Persona you get. The Persona you attempt to fuse will have its own spells but can inherit spells from previous Personas sometimes this works great but other times they can be less helpful. Maxing out a Social Link also unlocks the Ultimate Persona of the respective Social Link. There's also a bonus Persona based off the starter Persona Orpheus refered to as Orpheus Telos if you manage to max out every single Social Link this extremely powerful Persona is your reward.
In summary, Persona 3 is a great game. Great story, great characters and (what I assume is) great gameplay. Persona 3 any version really is worth getting.