Finally something I know a bit about.
BOWS
NOTE: All bows are rendered nearly useless if the enemy has a shield and they see the user drawing to fire.
Crossbows: Useless unless you know how to load, which takes 10 minutes to learn (nearly useless at level 0 skill, big jump by level 1). After that further training doesn't help too much (minor increase per level). Also long range shots are difficult because of the crossbow body getting in the way (huge drop off in hit% at range). Slow to load. Very slow (say 2-3 turns to reload). Also the crossbow tends to slow a man down more than other weapons.
Bows: Intuitive, start off with a pretty good effectiveness (okay at level 0). Practice helps a TON (good increase in effectiveness per level). Maybe a bit shorter ranged than crossbow, but at the same range they are easier to hit something with (greater hit% at range). Quick and easy to load.
Long Bow: Intuitive but takes a lot of strength to use correctly. Otherwise see 'bow'. Historically it was hard to field these units as the weapon is hard to draw and actually hit something with. This was not a skill issue so much as a strength issue (this is controversial, do not take my word for it. Try one...)
Hand Weapons
Mace/Club: Very easy to use (good ability at level 0). Skill doesn't help that much, more of a strength and footwork weapon (little effectiveness increase per level). Largely ineffective against armor, but also does not get stuck in armor which is cool. Very easy to make and pick up off the ground.
Axe: Also easy to use, but can hurt the wielder because the shaft is not balanced. So good damage at low level with moderate increase in safety with skill/level. Sort of easy to make, cheap to make, very common in fantasy/premodern settings. Hell it's common in modern settings. I have at least 5. Okay against armor, also the weight of the strike would make critical hits common at any expertise level.
Sword: As effective as an axe at level 0, but less effective against armor at low levels. Slashing is NOT effective against armor. Not at all. At higher levels thrusting is perfected and then you can take on armor very well. Most swords are also good at parrying melee attacks, especially Japanese swords. Axes are useless in that role. Historically swords were very expensive, but so superior that everyone coveted them.
Spear: Easy to learn (solid level 0 weapon) but without a ton of effectiveness gained at higher levels of proficiency. Valued for their length (hit 2 squares away?), one could stand off from a foe. Also thrusting is very conducive to unit fighting, but a TON of training and a shield is needed for that. Japanese Ashigaru (peasant spear) did not use shields, but then no Japanese really did. Most dungeon crawlers do not include entire units, which is where this weapon really shines. Good at piercing armor or dealing kill shots to the heart of enemies or beasts, this would require a small amount of skill and training at knowing where to strike (so CRIT with this weapon is learned later, but not too much later).
Pike: Nearly useless one on one. A unit weapon only. 2 or 3 times the reach of the average spear. Lengths depend on time period. Easy to learn individually, unit fighting is the main issue one must master. Like a spear just longer. The unwieldy length will slow a man down. Massively effective against mounted men that charge from the front, but the unwieldy nature of the weapon makes it hard to change facing, so a quick horseman could hit from the side and gain massive advantage (CRIT!). Against footmen, or in a dungeon, a good kill shit is nearly impossible to land (low crit rate even at high levels).
Halberd/Polearm: Massively popular during medieval times for the foot soldier. Almost as easy as a good axe to produce, these death on a stick weapons were also fairly easy to use effectively. Used in 2 hands, with good length, an advanced user could not only slash (level 0), thrust through armor (low level technique) but also snare with the hook and pull knights off horses or trip up armored men (higher level move). The issue is that shields were not often used with this weapon, so bow fire could really do a lot of damage.
SOME OTHER WEAPONS
Daggers - Easy to use at low level but low damage. AT higher level one knows EXACTLY where to hit and at what angle, so crits are huge. Short weapons, so you need to get in close. In game terms it means you need to catch someone unaware in order to score a critical/mortal blow. Daggers in Russia are used to kill bears. You just have to know where to thrust. Google it. It's true.
Flails - Have a great range and radius of attack, but require a ton of dexterity to use. Useless at lower levels of skill. Very good against unarmored assailants. Very weak versus armor.
Short Swords - A surprisingly hard to use weapon. Low level use includes slashing, which is largely ineffective with this weapon, at mid level one starts to learn the thrusting and kill/critical areas on the enemy. The elite level users could use this to parry melee blows, but only the elites. The movie Gladiator is a surprisingly good show of this. Note that this weapon is short and super accurate to wield, so an unsuspecting enemy can very easily get critted just like a dagger.
Great Weapons - Huge clubs, Great Swords, No Dachi and the like. These are low skill weapons. Practice as much as you want and you'll not get better at using them. They are all about strength, not skill. So level gain yields little additional effectiveness. They are of medium effectiveness against armor, but not due to thrusting. These weapons are nearly useless for thrusting. They are just so heavy they can stun an armored enemy, who can then be dispatched in a variety of ways.
Okay that's enough for now. I was going to get into more esoteric weapons and early gunpowder weapons but this is enough for now I think.