Advance, Bulwark, Charge, Disperse

Combat systems in games are an interesting, and usually complicated, thing. There seems to be a spectrum between tactical vs. narrative combat, with some systems lying in-between. Typically, tactical systems utilize miniatures/counters/tokens/pawns* ("meeples") of some sort, either on a grid (square or hex, usually) or grid-less.

An intermediate system would be something linear, based on range charts and the lines of battle that have characterized much of the history of warfare. Even horticultural or pastoral tribes often have a kind of ritual "war" based on lining up the men of the disputing tribes and throwing blunt weapons until one side flees.

Inspiration credit goes to the podcast Hardcore History, reading A Song of Ice and Fire, watching Master & Commander, etc.

*Note: I like to use snack foods to indicate fodder enemies, letting the player who lands a blow eat the snack item. Very satisfying.

Ranges: Long (sniping/parabolic fire), medium (direct shot), short (thrown implements), skirmish (polearms), melee, breakthrough, away.

Battles have often been won by breaking through the enemy's solid front ranks to get at the less-protected troops behind. These ranges are relative, not absolute, based on the current positions of the player characters.
As the player characters are the stars of the show, the battlefield should mechanically revolve around them, not the GM's attempt to narrate their version of the Battle of Five Armies. The GM should briefly describe what's happening around the PCs, but not roll dice for events that are NPC only. 

1. For example, in a typical medieval battle, the opposing armies first line up across from each other, just out of parabolic bowshot range. Perhaps siege weapons lob dangerous things across the gap, perhaps there are cavalry feints or runs on baggage trains. The PCs can do any of those. Better yet, there are proclamations by leaders of these armies (sometimes these are also heads of state). Duels of honor occur here. PCs should take part in this, maybe against their counterparts/evil twins/etc. 
2. Then, archers advance to rain arrows down on the other lines, shields are raised, etc. If one side has a massive advantage in archers (Achemaenid Persia, 100-Years War England, Eurasian Steppe peoples) the other side will have to decide whether to sit and take it, advance under cover of shields, outrace the barrage by charging, give ground, or take cover. Maybe the PCs will get to be at the vanguard of the charge, or will be given the responsibility to find suitable terrain to follow for a flanking attack to disrupt the archers? Or just give the PCs a few rounds to lob arrows/bullets/spells onto the poor saps 100m away. 
3. Finally, the archers withdraw behind a wall of shields and polearms and the armies come toward each other, either at march or by charging. Melee ensues. Chaos, blood, mud, gore, cacophony, etc. Players should not be allowed to communicate much over the tumult without helmet radios, psychic bonds, etc. Perhaps they have a simple system of gestures worked out, or a prearranged routine for taking down particular types of opponents. No plans survive contact with the enemy, and communications from the general take the forms of trumpets, drums, semaphore, etc. (Like the average peasant is going to pay attention to a flag 200m behind them when an Ogre is trying to rip their legs off!)
4. Eventually, one side will break. Whether it's due to a flank, felling of the commander, dipping a standard, stampeding elephant, appearance of a demon, whatever! The side that breaks will attempt to flee. Many of those fleeing will fail to do so, as most casualties will occur at this stage. It's a lot easier to stab a running person in the back than when they're trying to stab you also. Cavalry/centaurs/fast-attack killbots pursue and kill or capture (for sacrifice or food or specimens). 

Maneuvers: flank, ambush, take cover, charge, engage, disengage, chase, subdue, lock shields, rally, intimidate, cover flank, schiltrom/testudo, drop stakes/caltrops. 

These are just examples. Come up with more of these. More experienced troops that have served together for more seasons will be able to do more of these successfully. 

From a cursory reading of military history, the performance of a warrior is based primarily on training and equipment. Of course, luck and circumstance are also important. 

The following are various categories that came to mind during a brainstorm. These categories are vague outlines based on the amount and kind of training received, with their (arbitrary and semi-random) relative worth compared to other categories...

Levy/Rabble 1d6 = Tools as weapons, or semi-improvised. Little or no training. Clothing as armor. Will sometimes scavenge from the dead if allowed to do so. Bonus if defending their homes.

Militia/Trained 2d4 = Actual weapons, albeit basic ones that are easy to maintain in the field. Armor with maybe some metal (studs or scales over vitals). Animals for logistics (mules or donkeys probably). Group practice/drill regularly but not often. Perhaps they get together sometimes like most Classical Greek city-states? 

Men-at-arms/Professionals 3d4 = Fairly uniform gear. Unit identity/loyalty (Nickname? Standard? Uniform? Signature battle-cry?) Usually mercenary in nature. Drills as a unit frequently. May have a 1:1 soldier:mount ratio for battle and for carrying gear. (Medieval sergeants, most modern soldiers)

Caste warriors 2d6 = Trained from an early age, often individually (or for individual combat). Glory-seeking. Retinue present. Sometimes impetuous. Culturally or tactically-ideal gear. Bonus to attacking. (Knights, Samurai, Spartan Hoplites, etc.)

Elites/Fanatics 2d8 = Fueled by faith, drugs, etc. Impetuous. Fights to the death. Inconsistently-equipped, or with holy weapons. Bonus to defending holy sites or attacking heathen holy sites (Training is variable. Their main advantage is the ability to fight to the death. Great for delaying actions!). 

Veterans/Grognards 3d6  = Remnants of standardization. Will to survive. Superior coordination. May disobey unwanted orders. Bonus on the defense. (Trained by surviving multiple battles.) A well-oiled machine forged in the fires of many battles. 

Could this be adapted into another system, perhaps as a hack for those who do not have large enough tables for a good battle-grid? Perhaps. 
Feel free to respond and add to these thoughts.