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Grinding is largely unnecessary, and the "Hall of Giants" is a terrible place to do it, anyway. You can get through the game quite smoothly by taking more deft advantage of its mechanics, such as the fact that the character at the "top" of your party will take the bulk of the enemies' hits, and you can swap characters in and out of that position at will. Things like that.
Yeah, I understand the top and bottom thing, but I still get mauled by standard enemies whenever I go somewhere new, even though my equipment is top notch (thank you ship puzzle :)).
Once you start getting the items that cast spells, the game becomes much easier and its easy to blast through. I usually only grind for gil, once you get the full amount for the best piece of equipment or all the spells you need, you find you don't need to grind for levels. Its difficult to explain the story you will be missing cause its pieced together by the people you talk to and the places you go. Its finally conclusion is when you meet Chaos and see the ending.
I'd say give up playing it straight through and take it in smaller bites while playing something else on the side but if FFII is your next title and you can't finish FFI, you may want to skip to the SNES era cause II and III are very similar to FFI in the sense of being grind heavy and exploring more than seeing story. While they are not as bad as FFI, if you are here to see the story, you might want to just read them on gamefaqs or wikipedia cause the titles are more gameplay-oriented than plot-oriented.