FFI requires rather little in the way of strategy. The most important basic strategy is to place a healer (White Mage or Red Mage) behind at least one tank (i.e. Warrior). Only one healer is needed, and the White Mage is superior to the Red Mage for this. This enables your party to stand up to the HP loss of the mostly physical attacks your enemies will throw at you while keeping everyone in the fight. The lead Warrior is the only party member I consider essential, though one would be wise to always include a White Mage. The primary value of black magic is not in the elemental attack spells but in the buffs. Having at least a Red Mage capable of casting Temper and Haste as melee buffs is critical for the special dungeons.
The more astute reader may notice this basic strategy of support buffer/healer (and in other games ranged attacker) behind a defensive wall of tanks is a central strategy of a lot of games and even applies in a military context (though in the dynamic environment of the modern battlefield medical and other support such as forward observer fire callers is often integrated into front-line units). Due to its prevalence, this strategy is intuitive but may not have been to original players of such an early and seminal game. One should not take it for granted.
The formation system does not allow you to truly place player characters (PCs) in the rear. All are in line up front, but those at the top of the formation will tend absorb the most abuse. I suppose this is meant to simulate a proper ranked formation, which the enemy NPCs are in, so the designers were somehow able to animate that with more richly-detailed enemy models. I’m not sure what explains the design choice, but old RPGs required some charitable imagination on the part of the player.
Party selection is the key to the game’s difficulty. A player can titrate up or down the difficulty by selecting a different combination of characters. The characters classes to choose from are: Warrior, Thief, Monk, Red Mage, White Mage, and Black Mage.
[A Mathematical Digression. The cardinality of a full party is four. For fans of discrete mathematics, this gives us an unordered set of six from which we are to choose a sample of four, where members of the unordered set can be chosen multiple times. This situation is known as a “combination with replacement (allowed).” The total number of combinations of six chose four with replacements equals a whopping 126! I’ll leave it as an exercise for the reader to diagram this out himself as a demonstration. The formula is not overwhelmingly complicated but difficult to do justice in text. Its proof is by no means trivial.]
Out of the 126 possible party combinations, the strongest and most balanced is probably the {Warrior, Warrior, Red Mage, White Mage}. This gives three characters with decent physical attack and defense (and most fighting in FFI is melee), access to most of the useful Black Mage spells for most of the game, and a competent back-up healer to White Mage. The game is rather easy with a party of this combination. For a more challenging experience, try a play-through with a set exhausted by Monks.
As far as battle tactics go, there is usually not much to think about. It is good to have a black magic user for those occasional enemies that are highly-resistant to melee damage. Other than that, most enemies can be dispatched with physical attacks. With full enemy sets of nine, one may want to use some attack spell they are vulnerable to in order to move the battle along quickly and not absorb too much damage. The only real risk from random encounters are primary status effects abilities/spells or secondary status effects from melee attacks, such at the dreaded Cocktrice’s ability to cause Stone secondary to its melee attack. These are especially problematic in the middle game before the player has a mature White Mage that can reverse any status effect. Stock up on curative items before venturing into dungeons. Even in the most difficult battles, the tactics of developing the PCs with defensive and offensive buffs followed by plugging away at the enemies’ hit point counters with physical damage and healing regularly is rather straightforward. Most enemies that pose any real threat are fairly immune to status attacks, though some can have their bite taken away by being slowed. Other than that, there really is not much to it. Strap in for a slow grind.