Turn based RPG's are easily my favourite genre.
Besides the story's are not the same, they follow a similar path. Each major Final fantasy ends in a different way, I still think that Final Fantasy 6 has the greatest end boss out of any game I have played, especially with it's 18 Minute organ boss theme, impressive for the SNES.
There is alot more to it then just a "boring" turn-based battle. It's to improve your character, gain items, money, weapons & armour. Its more strategy than action, you decide which character has what, whether it will improve the character or if it improves the aid of one. You decide if he will focus more on offence or defence.
The more battles you have the stronger you get, it becomes easier to kill a same monster and it becomes easier to beat the game. If you do not train enough, you will end up getting destroyed by bosses!
If I were to recommend a Final Fantasy game, I would choose 6 or 7. The choice is simple, 6 if you want to play one of the greatest 2D JRPG's as chosen by fans, or play 7 if you feel like a beginner to the world of turn-based RPG's, it's a great game and it converted many people into JRPG fans.
Although if I were to recommend you a turn-based RPG which isn't Final Fantasy, I would say Chrono Trigger, Mother 3 or Lufia 2, which are all amazing games with great story.
Sorry if I wasn't in depth, but its really more of the player thinking of the battle than any action.
Although to play a turn-based RPG you have to be devoted and interested into the storyline, if you don't like the game you are playing, you will end up giving up half way.