Let's see...I'm going to try and not repeat what others have said too much. Everyone else has covered anything I could have said for Chrono Trigger or Final Fantasy VI. The other game series I have either barely played, or don't know enough to give you an opinion. So I'll be covering Star Ocean, since no one else really covered it that well and then giving you recommendations for other RPG series to check out.
Star OceanI have never played the first or fourth one, but I have played the second and third.
Star Ocean 2 lets you choose between 2 different characters to play as, Rena or Claude. While you cover the same storyline with either character, you get different scenes and options depending on which character you chose. You also find out about which character's you chose background more in detail, so you get more information about whatever one you chose. Another neat thing is that depending on which character you chose, you get a different party member at a certain story point. Otherwise, all the characters (optional or storyline important) you can get with either character. There is also so many different choices you can make in this game! Like not being able to recruit certain characters if you recruit other characters, and you can even influence the ending. There are a ton of different endings in this game, based on which character is closest to you. So you can pair yourself with any character. As for the battle system in Star Ocean 2, if you have ever played any of the games from the Tales series, it plays a lot like them. You run around the battle field to attack your enemies. Oh, you also do not have to stick with playing as the character you chose for battles. You can swap and use any character you want to play as in battle.
Star Ocean 3 (Or Star Ocean Til the End of Time) is pretty much it's own storyline, and you do not need to play Star Ocean 2 at all to understand it. Like Star Ocean 2, you have the option to recruit many different characters and make all kinds of choices. Like Star Ocean 2, there are many different endings based whatever character you decide to pair yourself with. The battle system is still the running around to attack your enemies. Really, you could go for either this or Star Ocean 2. Both have good stories.
Other Recommendations Someone mentioned the first
Lunar. I second this, but I would recommend the Lunar series as a whole (except for Dragon Song on the DS, stay away from that). I preferred the second game, Lunar 2 Eternal Blue, but I love both the first and the second game. The first game in the series is a lot easier to get a hold of since it has been remade a million times. The original was released on the Sega CD (Lunar the Silver Star), but later it was remade for the PSX (Lunar Silver Star Story Complete). Then it was remade for the GBA (Lunar Legends), and then recently, it was remade for the PSP (Lunar Silver Star Harmony). As you can see, the first game changes its name with every remake, lol. I liked the original Sega CD versions of Lunar 1 and 2, but the best versions are usually argued to be the PSX versions. Lunar 2 was only released for the Sega CD and PSX (remake). The characters and story are pretty good in this series. Plus, Lunar was one of the first RPGs to use animated cutscenes (1992). The battle system plays like a traditional turn based RPG.
Someone also recommended the
Shin Megami Tensei series. I also recommend this. Usually people play the Persona games in this series, which the 3rd and 4th games are amazing. You play as a silent protagonist in Persona 3 and Persona 4, which give you room to make any kind of choice you want. However, if you choose the wrong choices, you can mess up relationships, which are an important part of powering up your character. So while you can have fun with relationships in this game, you also need those relationships. The SMT series has a whole is turn based. However, it is turned based with a twist. In Persona 3 and Persona 4, element type is REALLY important. If you hit an enemy's weakness, you can go extra turns and defeat the enemies faster. This also goes for the enemies, however. So you have to be careful. In Persona 3 and 4, you gain the ability to basically summon "the power within you" which takes the forms of all kinds of demons. The cool thing about the SMT series is that it has so many mythological references to demons. Shin Megami Tensei Nocturne is also an amazing game. Unlike the Persona games, you do not use your "own powers". Instead, you can recruit demons to join your party, leaving limitless possibilities. Also, Dante from Devil May Cry makes a cameo, who can be recruited as well, which is awesome. Elemental weakness are even MORE so important in this game that Persona 3 and 4. If you want a challenging, but really fun RPG, get Shin Megami Tensei Nocturne.
Okay, I'm done now. This post has gotten too long.
