Star Ocean is similar to Final Fantasy on the surface in that it's a Japanese Role Playing Game, but under the hood they're two completely different animals.
It was created by Gotanda Yoshiharu who was also the started the Tales series. Tales of Phantasia was radically different than the Tales games of today. It still had the same basic real-time action style, but was much more simplistic.
After some disagreements with Namco as to the direction of the series, he left and took some of his team with him and founded Tri-Ace. Soon after, TA was gobbled up Enix and became another on of its gazillion subsidiaries.
That's when he and his team started work on the Star Ocean game.
From there, the game play evolved quite differently. Where the Tales games have become almost fighteresque in their control, speed, action, and mayhem, the Star Ocean games have stayed closer to their roots. The games still have an action feel to them, but it's slim lined, less complex, and a bit "slowed down." They are also a bit more turn-based.
Story wise, Gotanda is a self-proclaimed hardcore Trekkie--especially of TNG. A lot of the terminology and philosophies are similar. For instance, his "UP3" is almost the Prime Directive verbatim.
That's actually the core of the game. For instance, most of the stories take place on Medieval/Feudal like planets, so a lot of the focus/theme of the stories is how much the main characters should/have to "get involved."
There's also some sound effects "borrowed." One glaring example is the LCARS PADD "beep."
The first Star Ocean game was a very late Super Famicom (SNES) game. It was never released outside of Japan.
It may have come out late in the system's life, but it was technological marvel. So much so, it was significantly better than a lot of early Playstation games.
The down side, however, is that, since they tried to pack so much into the cart, it had bugs galore. I'd even go out on a limb and say it's the buggiest video game ever made. A lot of it was memory related. The problems got so bad that it was uncommon for people to completely loose their saved games--a real downer for those who were at the final dungeon.
Another revolutionary aspect of it were the "Private Actions." When entering a town you could choose to "split up" and thus interact with the other characters independently. This resulted in various different scenes, romances, and friendships.
There was also the item creation. Each character has a set of innate "talents" that relate to his or her ability to cook, paint, write, etc. They then can become more proficient in various skill sets that worked in correlation with these talents. Through this, you could create various healing items, weapons, food (For mass healing.), and other miscellaneous items for combat use.
There has since been an excellent fan translation made for ROM use, however the bugs are exacerbated with emulator use. I've completed the game several times, but excessive and multiple saves were pretty much necessary.
Star Ocean: The Second Story was released for Playstation and carried outside of Japan. It's been hailed as of the best JRPGS of the PSOne era. It supported beautifully colored graphics, branching story lines (Two separate "main" stories that took different directions.), and many different characters to collect.
The Private Actions were spruced up. Character relations would now even have an impact in battle. For instance, if character A (who was a healer) didn't like character B, th AI might wait until he's near death before healing him. The effect of the spell would also be lessened.
Item Creation was also improved. There were more skills added, and the number of different items that could be created was literally in the thousands. The tediously addictive Pick Pocket skill was also added.
The hero could now run throw towns and try to rip-off the NPCs. You could collect a whole slew of different items--so of which could only be obtained through pick pocketing. Some of the reactions you would get if you failed was hilarious.
Both games have since been given remakes/updated ports on the PSP. I haven't played either yet (as I don't have a PSP) but I hear they are both excellent.
Star Ocean 3 was a PS2 game. The Directors Cut of the game was hailed as the game of the year. And considered to be the best of the series.
Because of the Square/Enix merger, the game now sported the classic Square uber-graphics with FMV eye-candy galore.
Both combat and item creation were derastically changed. Combat was now more involved and at times overly complex. Item creation was now done, instead of by the party members, by various NPCs you could find and "contract."
To recruit them often meant meeting various requirements. They could also be signed by "others" so you'd have to wait for their contracts to run out. The become more cumbersome than anything, because in many cases you'd have to excessively backtrack through long, tedious dungeons just to find them.
While the game is still a lot of fun and certainly a great game, for a lot of us it was void of the charm and "Fun" that made SO:TSS so great. Many a flame war has been ignited over which is better.
Star Ocean 4 was launched for the XBox 360 earlier this year. I haven't played it yet, but it's been panned by a lot of long time SO fans. Of course, there is a small fraction who think it's the best yet. But, I really don't know too much about it.
My recommendation would be, if you have a PSP is to start with the two remakes. They should be pretty to find and fairly inexpensive.
SO3 is also a great buy for the PS2. But, at this time, you might have to look for it a bit.
If you're looking at SO4, I really can't say one way or the other. I haven't played it, and, while most reviews have been less than good, I want to reserve my opinion for when I give it a fair shake.
If you're worried about story connectivity, don't be. Other than the first two, there isn't any. And, even in that case, the only real connection is the protagonist is the son of one of the characters of the first game. The stories are completely independent.