Considering Spartans primarily used their spears over their swords and how they were a feared military power in their hay day, you might be wise to not underestimate what a man with a polearm can do. Keep in mind, it's not just the spearhead that's dangerous; you can use the length of a spear as a makeshift quarterstaff and I promise you're not going to have a super easy time knocking a spear out of the way for a kill when the enemy is quite eager to keep it trained on you. You knock it aside, he pulls back and thrusts at you, prompting you to react or get a foot of steel in the guts.
The main advantage of these longer reaching weapons, is that rarely is your body in any danger. Most of the combat is kept just out of arm's reach, leaving you free to use any strategy you choose. The main disadvantage of a polearm, spear, or other long weapons are that when people close the gap, and get past the head, you no longer have the ability to re-position the spear to strike in a manner that would wound your foe.
Against a swordman with a shield, you will be disadvantaged individually; he will not have much to fear of your harassment, and will simply be able to bide his time and let you wear yourself out. In a formation, especially phalanx formations that Spartan Hoplites used, it was exponentially harder to get past the tips of spears; this is where most of their success lay. A pole-axe may have the advantage in that you could hook your opponent, but that isn't going to protect you if they're already lunging at your ribs, which is often the goal of someone that's gotten close to you.
With a large shield, you have to use a smaller spear in a single hand, cutting some of your ability to re-direct the weapon, as well as some of your reach. The more effective the shield, the less effective your spear. Taking this sort of set-up would leave you disadvantages against your other foes; inversely, with larger pole-weapons, you would be more vulnerable to projectiles from the archer; if you could use a shield at all, it would have to be much smaller, leaving you disadvantaged against the knight.
My choice would be a flanged mace with a spike at the tip of the shaft, a ball-ended morning star, or a
goedendag and a heavier steel shield, and a good suit of armor. If I had to pick any secondary weapons, it would be as many Greek Fire hand grenades as my belt could carry.
The shield would prove excellent at repelling the archer's shots, allowing me to advance without too much fear of serious injury, perhaps a few bruises. Even if he came with a crossbow, a sturdy steel shield, particularly rounded ones, would prove extremely valuable against him. If the bolt could penetrate the shield, as if the crossbow was fired point blank, it would still be stopped by heavy armor. Eventually, I would catch him or he would break or lose all of his bolts/arrows. In close quarters, with only his light weapons remaining, he would be doomed.
In individual combat, a heavier weapon, like a mace or hammer and a shield can be used to deflect or parry a spear, since they are not often held in a manner that prevents them from being glanced aside. All you would need to do then, is get past the tip and strike with enough force - even without solid blows- to break an arm, rib, or leg, incapacitating the wielder of the spear. Even if they took a large, wooden shield, the superior material of the mace, as well as it's weight, would still deliver enough force through the material to break bones.
Against the knight, you could break a leg of the horse, using it's own momentum against it, and remove his advantage of height. The horse cannot protect itself; you would not need to worry about an accurate attack against it, only protecting yourself; maces and morning stars often do significant damage no matter how they strike. They were used with great success by peasants throughout history to kill mounted knights, like in the Franco-Flemish War.
Against the swordsman? Any of my three choices of mace would have an advantage against him. I could cause him harm in a greater number of ways than he could cause me.
In all circumstances, setting whoever I'd be engaged in combat with on fire would be cruel, although devastating. Lighter armored foes would go up in flame pretty quickly if hit, or would be forced to back off and go on defense immediately; heavier armored foes who have a harder time dodging would suffer serious burns from the heat, inhibiting their ability to fight.
