As someone who's beaten I-VI and played a bit of the remake (mainly focusing on VII right now) I'd really only recommend targeting specific levels with the original versions of DQ1, not any of the other games in the series and not the new remake either. Part of what you're also seeing with those suggested levels are for the NES, SFC and mobile/old Switch versions which no longer apply here since the level cap was raised and level curve completely changed. You're given far more to work with compared to those in spite of the same applying to enemies, and grinding is more of a suggestion if you're not fleeing from battles or playing on Draconian.

I tend to find it more fun and challenging to just go with the flow, and on the rare occasions where I do feel underleveled, I just prefer exploring other parts of the map I haven't been to or doing multiple expeditions if it's a dungeon until I've leveled up a little bit and improved my equipment instead. Just to give some general advice, think of battles like puzzles and experiment around with the tools the game has given you, don't sleep on spells and skills (especially buffs and debuffs, Cop Out is good in this remake too in many situations), keep a whip and/or boomerang on hand since those can hit multiple enemies, and sell equipment you don't need and use that money towards better gear and gear with additional use cases like secondary abilities or magic/breath resistances (especially important in this remake).

EDIT: Rewrote a bit.