Note: My only real advice to you in the game is to choose your magic spells wisely and not to train the ones you don't need. For a recommendation on the ones I suggest and don't suggest, check out the Magic list for more. Also, if you want an easy way to train, please check out Secrets for a hint on easy stats. Be sure to train here and there otherwise, so you aren't always weak. For a good base, make sure your HP is about 2,500 at the end of the game with your magic at Level 8+, same with weapons/shield and possibly 50+ for whatever stats you are training your characters in. By the way, do not - I repeat: do NOT - bother training your 4th party member, EVER.
They are NEVER with you for long, so do not bother with them. ONLY bother with Leon. Finally, if you're aiming for a perfect game, like 100% in bestiary, item collection and art gallery, just make sure you find every item and monster in the game and you'll be fine. For information on where each is located, please read the walkthrough below. As for levels/stats, I will make a recommendation, but it's totally up to you how you want to build your party up. Only use what I say as a guideline if you don't care for my opinion. Finally, remember the Inn trick: Heal everyone up with magic and then go to the inn to save on Gil, since the inn's cost varies on how much HP you need to recover and the same with MP.
Final Note: If you are playing on normal mode, BE CAREFUL. You cannot run, view the world map as "flat" or auto-target monsters, so it's just like playing the original NES version. Also, I will only at the top of each area suggest the HP you should have or want to train to. The rest is totally your call, as I have no idea how you'll want to train your guys. Also, I will not remind you to save your game. That is your responsibility so save and make memo files whenever you feel the need to. I can't hold your hand forever, you know :P.
So, yeah, thanks for reading all that and enjoy Final Fantasy II!