So I have been doing some research on HEMA for how weapons and armor work in the real world.
About the three attack types, slash, pierce and blunt:
Slash is good for any unarmored opponents. Piling a constant amount of wounds and bleeding will eventually exhaust an opponent. But if they have even a bit of armor it becomes completely useless.
Pierce is the most effective attack. On unarmored you can target vitals and on armor you can target the vulnerabilities. The most important thing to understand is that it revolves around accuracy or "critical". A dagger is the most accurate weapon, half-swording is also accurate. A spear can be accurate but the longer the reach used the less accurate you get. You can also use pierce inaccurately against unarmored opponents, this can be especially effective against multiple opponents. Pierce can have some degree of armor penetration but its not all that much.
Blunt is the most effective against armor. Against flexible armor like chainmail and brigandine its especially effective as the force is distributed into the body. On a rigid armor like plate mail its design to glance of shots and use its rigidity to stop the force entering the body. Blunt also does barely any damage to an active aware opponent. That blow to the head for a knockout is a pipe dream. Slog it off until one of you gets bored and dies.
Now the super secret cheat attack that is affective against everything is grappling. On a one on one it all comes down to who can wrestle first and put a dagger behind those brows. Disarm, disable, strangulate, smack all in a glorious mess of limbs everywhere.
Another super cheat attack is range attacks. Especially in ambush in which case you die, hope your games have dodging mechanics that makes you look like a ballerina because they are the few piercing weapons that do pierce armor and those are arrows. It might not outright kill you but you are off to a wonderful start.
Now on to the weapons!
Spears are your bread and butter. The concept of range is very important to understand. What it means is that if I have the range advantage I can threaten you and you can't threaten me. It also means I defend myself by you not being able to hit me. The cost of range is accuracy, while a spear can become more accurate based on the placement of hands and how leverage works that still necessitates a shorter range. Another concept is unwieldiness, based on the physical motions your arms and body makes and the distribution of forces your ability to manipulate a weapon can be limited, this can mean a penalty especially in defense as well as higher trade offs between speed and accuracy. A spear used at a shorter range has a lower speed because of the aforementioned unwieldiness, an opponent who closed the distance to a spear user has the advantage as long as he can maintain it.
A spear in one hand is fairly unwieldy, has no defense ability and very little accuracy.
Staves explores a very interesting concept that resides in spears. They have basically no damage, it can't even be considered a blunt weapon. However it still has range and shows the power to impede, distract and trip an opponent even if it has no offensive power. This means it can be a very powerful defensive weapon and explores the power of unbalancing an opponent. Like grapples a tripped opponent can be killed even if he was impossible otherwise.
Shields. If you want to take on a spear you better have a shield. If you don't have much armor you are going to have a shield. If you don't want to be a arrow ballerina you want a shield. You can negate attacks so that you can close in.
Swords are very good defensive and offensive weapons. They are specially designed for wieldiness. As good accuracy as your going to get outside of a knife. Unarmored opponents you can chop all day. Dual wielding is interesting in its ability to mange more opponents as you have more coverage that can both defend and attack. But you probably are better of with a shield.
Axes. Are a poor man's sword, quite true as it takes less metal and easier to make. They are unwieldy compared to a sword so no ability to defend and no piercing. It has the advantage in chopping things up and the shield is a great equalizer. It also has a nice trick where you can hook things like shields. Can work to impart some force like a hammer.
Pickaxes. Would be a absolutely great blunt weapon if a thing called weapon alignment didn't exist and hammers weren't simply superior. Technically it could have worked as a piercing weapon but I have not seen any historical evidence.
Hammers. Hammers are not flat, they have mini-spikes on them. You bash people with it. Its simply the blunt advantage.
Maces. Same.
Halberds. The goodness of slashing on a polearm. Chops those peasants up.
Poleaxe. The swiss army knife polearm OF DEATH. Bash, chops, pierce, hook in a shorter form then a spear for added wieldiness and accuracy and used by knights in full plate armor as machines OF DEATH.
Now as for the armors:
Paper armor - Armor made of paper. Defense value of 0.
Leather armor - Same as paper armor.
Peasant armor - Same as paper armor.
Cloth based armor - Using layers upon layers of cloth. Gives a surprising amount of protection. Not exactly cheap. The more layers it has the more you look and move like a penguin. Has some blunt dispersion like a pillow but not much
Buff coat - Based on raw hide. Similar to cloth based armor but slightly better. Historically more recent.
Silk armor - Same as cloth but triple the Fabulous!
Chainmail - Basically negates slashing. High cost because of high amount of time to make, putting every fucking individual ring over and over... Lower quality may be pierceable. The worst against blunt.
Loose plates - A wide variety of armors like brigandine that has plates at its base. Still bad against blunt. The best your going to get on the market. Usually worn together with a chainmail shirt below.
Plate armor - A walking tank invulnerable to all damage. Custom fitted for the person, probably needs the status/license to use and costs a fortune. Careful of nasty grapples and trips. Some more loose pieces can be on the market and some opponents might have parts of the armor.
As you can see the effectiveness of weapons is directly tied to how poor people are. Those bandits who have proper armor can be especially nasty. At least shields are cheap.