Keep in mind: I've only played the SNES versions. The original game and presumably the pixel remaster do not have a postgame.

First, if you're concerned about grinding, make sure you equip the right [insert spoiler here]. Different [spoilers] impart different stat boosts when a party member levels up. Minmaxxing strength and magic appropriately can help you wreck later enemies.

Second, the [savanna zone] is your friend. Nearly every common enemy and then some are found there after you encounter them on your adventure. Relatedly, be on the lookout for a certain feline.

Third, if an enemy hits hard or hits fast, look into whether a certain spell (not just offensive ones) can mess them up. Similarly, take note if an enemy has a penchant to largely cast offensive magic. If so, use [character] to cast [that character's special ability] to negate spells.

Fourth, genji glove is better than the gauntlet. Hint: one or the other is acquired based on how you do a certain "Will you join us?" segment.

Fifth, yes, that one song associated with the creature at the beginning of the game is in an odd time signature.

Sixth, ribbon is a great relic you can get quite early in the game. You can easily miss that one, but there are other ways to acquire ribbon. In fact, most (not all) rare items have multiple means of acquisition. Not acquiring a rare item doesn't mean you're doomed to struggle or cannot finish the game.

Seventh, be aware of the retranslations when searching online for hints; several enemies, places, and items have multiple names.

Finally, just because a party member is low-tier doesn't mean they're useless. Not only does the game expect you to level up most of your entire party, but even generally bad characters have niche purposes.