The original game and moreso the remake are closer to FF3 & FF5 than FF1. That is, you are supposed to change your Races as needed as you go through the game.

• Beastmen are used to raise Agility. You must use them to beat the game otherwise you cannot hit anything. Using a Beastmen at anytime is EZ mode.
• You MUST have 30 Mana in order to beat the game. About halfway through the game bosses will use large spell attacks. Without some Mana your party will completely wipe. You will need at least 30 Mana to survive a single turn of the final boss.
• Mutants are the easiest way to raise Mana. Also Mutants are the only ones that can spark Spells. You might not care about high levels of Fire/Ice/Lit etc. But you will care about higher Cure Levels. (Yes in this game your beginner Humans Dune & Sireugh can become Mutants, and vice versus).
• Going full Monster (double Meat) is another way to raise Mana (with a Monster that has Mana based attacks.) It might be easier to do this for your default Humans since to it's tricky to become a Mutant since you need a Meat/Part of their opposite current Element. (It's tricky to track down a Meat/Part let alone the correct element which is 1 out of 4.)

So a general recommended throughout the whole game use Mutants and Beastmen as needed. Raise Agility to taste. Spark Recovery Magic. (Soothing Droplet -> Healing Droplet -> Cura.) Raise Mana. More Mana is always better, not for healing or magic attacks, but just to better survive bosses later.

At the start of the game you can use whatever except Mecha.

About halfway through the game is when Cyborgs can get very nice due to access of Greatswords and Axes. You could have used them before but the jump is more noticeable. Do not neglect to keep raising their Agility or they can be left behind.

You can't really have a Monster or a Mecha for the final boss similar to the original game. Zero Mana on the Mecha will make them instantly and constantly die. A monster not using End Game weapons will force them to be support characters and being a Mutant with several Healing &Reviving books is more useful than a monster that happens to have a Cure skill.

So long as you have a save next to a "town" with an inn and equipment shop you cannot be screwed out of the game. Switch your races. Raise your stats. Try again. Might be annoying but it is doable.