Mechanics of Battle

The most important thing that you should always have is balance. Try not to have too many of one type of soldier in your army like centaurs or archers. You should always have at least two wizards, one healer, one archer (except towards the end of the game), one flying character and a couple centaurs. Keep the weak members of your party towards the back and the stronger ones towards the front, but don't keep the weak members too far behind or else the stronger ones will hog up all the experience. Remember to always try to build up your leader. If he's too weak then he'll die easily in battle. And if he dies then you have to start the battle all over again.

Building Up of Levels

When a character gains 100 experience points, he or she (or it) gains a level and random aspects of their stats grow stronger (HP, MP, strength, defense, etc.). Most of the time their stats don't raise much but sometimes it raises a lot. It's very important to do plenty of what I call training battles. The point of a training battle is not to complete the battle, but to almost complete it, cast Egress, and start over so that your army grows stronger each time you repeat the battle. When a new character joins your army (all of the rookies start out at a low level), do several training battles having that character be the only one to kill the enemy. Just use everyone else to weaken the enemy only to have the weak rookie hog up the killing's experience.

Annoying Yet Sometimes Useful Terrain

The terrain decreases the movement span of your characters, but it also helps defend them from enemy attacks. The terrain gets the most annoying when you battle in large forests or large desserts. Most of your characters end up way behind while a few of them, who aren't effected by the terrain, end up far ahead. Try your best not to have that happen because if a character wonders off too far and gets heavily weakened by enemy attacks... then no one could hear his scream. :o

Ever-so-useful Items

Each character must have at least one or two healing items in their 4 slot inventory. It's a good idea to keep one slot empty for each character because you never know when a defeated enemy will drop a rare item. Well actually you can look at an enemy's inventory, but like you're going to take the time to look at each enemy in every battle. You can't always predict what happens in battle, so when a character comes close to death, the healing items could save the day when your healer can't arrive in time. Equip the strength boosting ring and the defense boosting ring to the characters who need them most. Take advantage of special items like those that allow you to use them during battle. Be careful though, use them too much and they disappear. The only exception is the Sword of Light, the Sword of Darkness and the Chaos Breaker, they don't disappear no matter how many times you use them--take very good advantage of them!

Enemy Armies

Some enemy armies have a leader just like you do. And if that leader is defeated then so is the rest of his army. It's obvious who the leader is since it's the only one of its kind compared to the rest of the enemy soldiers. However, I don't recommend killing off the leader unless you really have to because you could use the experience from all his enemy soldiers. Kill off enemy mages, priests, archers, and robots as quick as you can. They can get really annoying.

Advantages and Disadvantages of Character Classes

Take advantage of your wizards when you're fighting strong enemies. Their magic always weakens the enemy with about the same amount of HP. That can be an advantage toward strong enemies, but a disadvantage toward enemies that could be easily defeated. Archers are useful throughout most of the game in forest and dessert battles, but towards the end of the game they're not useful due to their lack of strength and defense. The same thing goes for birdmen. Centaurs are oddly balanced characters. Some have good defense yet poor strength and some are strong yet have poor defense. Earnest is the only well balanced centaur.

Recommended Characters

The fighters that I highly recommend to have in your army are Zylo, Guntz, Kokichi, Musashi, Bleu and either Gort or Earnest. Around the middle of the game, having 3 or 4 centaurs in your army would be a good idea. Zylo, Guntz, Domingo, Kokichi and Bleu are great for those annoying forest battles. Well that's it. There isn't much to say about the fighters. They just... fight.
Tao, Anri, and Domingo are great when their Blaze and/or Freeze spells reach level 3 and level 4. Domingo is even better since he can fly! If you train him right then he could have the most HP, most MP and best defense than any other character in your army. Those three magic casters play a big role in the last battle since their powerful spells kill Dark Dragon in just a couple rounds - so they are a MUST to have! The fourth magic-user, Alef, isn't really too good. She does learn strong Bolt spells but towards the end of the game (when you get her) they aren't too useful.
I can't recommend just one. Each healer has their own advantages and disadvantages. Lowe is weak but he can learn up to Heal level 4. What really sucks about Lowe is that he doesn't learn Aura. Khris and Gong have a tolerable amount of strength and defense but they don't learn that many spells and their spell learning rate is slow. They both eventually learn Aura but only up to level 2. Torasu is very similar to Lowe, the only difference is that he actually learns Aura and up to level 4 too!! It's a big pain to build up his low status, but it's worth it.