Golden Sun and Golden Sun 2 on the GBA. Traditional JRPG combat. But you can catch djinns! Equipping different Djinns to your character gives them different stats/spells. Quite Good. There is Golden Sun Dark Dawn on the NDS, but never played that.
Fire Emblem and Fire Emblem the Sacred Stones on GBA. Fire Emblem:Radiant Dawn on Wii. IT is a strategy RPG where you can recruit tons of characters. TB battles and all weapons / spell books have limited durability. Very fun. Note that I haven't played Radiant Dawn yet.
Atelier Series. Titles can be found on NDS and PS2 among others. Fun time management/slice of life jRPG with TB combat.
Disgaea DS on NDS and Disgaea 2 on PS2 or PSP. Strategy RPG with very fun mechancis like lfiting/throwing, master/disciple, reincarnation and senate. Lots of recruitable unique characters or creatable human/monster characters. MC is fixed though.
Grandia on PSX and Grandia II/III on PS2. This is another fun jrpg. Combat is TB with time units kind of thing. Weapon skills/ spells level up by use. and combination of different weapon / spell levelups give special skills. Very fun combat. Haven't played Grandia 3. Highly recommend Grandia though.
Jeanne D Arc on PSP. Strategy RPG in medieval European setting. Quite Good.
Star Ocean on SNES (and its remake on PSP) also quite good. You can spend skill points to customize your characters. Recruitable party. The SNES version plays like a TB game but has a clock running and game pauses when your turn comes.
Star Ocean 2 on PSX/PSP. has real time combat on a 2d battle screen. And Star ocean 3 is a piece of shit so stay far far away from it.
The Legend of Heroes Series on PSP. The Legend of Heroes : Trails in the sky out for PC too. I found the characters in trails in the sky a bit annoying. but trails in the sky has a good gem/magic system along with TB tactical battles.
Eternal poison for PS2. This is one of my favorite strategy RPGs. There is no grinding/repeatable battles so it is difficult. To get the real story you have to play through multiple player characters. Each player character has his own unique party members and gets a different view of the plot. All MCs have with generic class based recruitables.
Final Fantasy Tactics (on PSX / PSP) / Tactics Ogre (SNES / PSP) / phantom brave (PS2/PSP) are strategy rpgs. Out of these 3 storyfags should definitely play the PSX version of Final Fantasy Tactics. Tactics Ogre is more strategy side but very good none the less. Phantom Brave is inferior to disgaea but still fun me thinks.
Elminage Original and Elminage Gothic on the PSP. Wizardry like Dungeon Crawler. Fucking Awesome. TB Menu driven combat. Gothic on PC too.
Breath of Fire 1-3. Standard jrpg but you can turn into a dragon! (3 on PS2 others on SNES) 3 has fun little touch of masters. your player can accept an npc master to elarn new skills and influence player stats.
Breath of Fire 4 on PS2 is different from other breath of Fire series games. your dragon powah is a curse. You get OP if use dragon powah, but it eats your life. Use dragon powah too much and its game over. Oh and mindlessly walking around too much also minutely fills your curse meter (but can be mostly ignored if u use dragon powah only in boss battles)
Bahamut's Lagoon on SNES. it is a strategy rpg. where you move small parties around a map. final combat is jrpg TB. Think of SMT Devil Survivor types combat. you have pet dragons and feed your dragons anything to influence their stats and evolutions. Oh the female lead is a total bitch, and PC's mentor tries to show homo love. Lots of different classes and really fun gameplay otherwise.
Earthbound for SNES. JRPG with a lighthearted story.
Lufia / Lufia 2 on SNES. Fun JRPGs.
Tales of Phantasia on SNES. Battle screen is realtime 2D and actually works decent with controllers. You can give it a try.
Also among the titles recommended, I would second SMT: Nocturne, SMT: Strange Journey, Legend of Mana, Final Fantasy, 7th Saga (but use one of the 7th Saga+ hack in that case or its very annoying), Etrian odyssey II (and II and I), Seiken Densetsu 3, Dragon Quest 9, Suikoden Series, Infinite Space. haven't played rogue galaxy, vandal hearts, brigadine or Arcana but looks fun.
Thats all i can recommend form the top of my head. Not all of the recommendations satisfy all your requirements but they are good jrpg titles anyway.
One Exception is Elminage Gothic / original which have character creation and fully customizable party and very good exploration but they are wizardry style dungeon crawlers.