Many many of the Final Fantasy games have fairly simple combat systems and enjoyable characters/storylines. FF8 is probably the most confusing, so I'd avoid that, but 9 or 10 are great choices, 7 is the revered classic, and 4 and 6 are great in my experience. I wouldn't try to convert anyone to JRPGs with 12 or 13.
Tales games are great because the combat is the most action-oriented of any series I've played. If you don't like anime, the characters can veer dangerously close to some obnoxious stereotypes, and the stories tend to spiral into incomprehensible nonsense, but the gameplay is always fun and there are tons of sidequests.
In my little experience with Star Ocean, (just the new one, The Last Story), it just seems like a worse version of the Tales series. Action based combat, but really grating characters and average story
Earthbound is very funny and creative. The combat system isn't very complex or engaging, but the experience, with the goofy characters and great music and just bizarreness of it all, is totally worth a look.
I'd avoid the Disgaea series. It's funny and has good stories, but the game has a lot of depth that it expects you to explore, there are LOTS of numbers to consider that are never adequately explained, and lots of grinding is expected of you. A good game, but not one to start with.
The Persona games are my personal favorites. It's very Japanese, but in a reasonably authentic seeming cultural way rather than an anime way if that makes sense. The characters are what make these games, as they are very well written and fleshed out. The music is killer, and the stories are great. The combat is straightforward, but they developed their own language for spell names, which can get confusing, and the game can be brutally unfair, like gettting a game over from one unlucky attack unfair. I'd recommend Persona 4 because they do a better job with the characters in my opinion, and they also introduced a couple changes that reduces the cheap deaths. They also have an easy mode that gives you some extra lives.
If you have a DS or GBA or something, Golden Sun is fun, simple but flashy combat with a good amount of customization, and good puzzles and exploration factors. However, the newest one (Dark Dawn) is probably the weakest of the bunch, and the best (The Lost Age) is best experienced after playing the first one.
All in all, I'd recommend Tales for the funnest battles (either Symphonia if you can or Vesperia), or Persona 4 for something unique and very engaging, even if there will be a decent bit of culture shock. Final Fantasy games are consistently very solid if neither of the other two seem up your alley
