If we were to be technical, the best overall melee medieval weapon is the halberd. It was a versatile weapon near the end of the medieval ages and on to the renaissance, as they have the range and leverage of a spear or pike, cutting power of an axe, stabbing power of a lance, can be used in tight formations as deterrent for incoming charges, and in some designs they may also have a small hook to drag mounted enemies down to the ground.
Although each medieval weapon has their uses:
- Regular spears, axes, and clubs are cheap weapons that can be equipped by anyone and are cost effective.
- Pikes are used as deterrent against infantry and cavalry charges while holding a position.
- Spears are more preferred than swords, due to their range and power.
- Axes, Hammers, maces and clubs are the best way to counter heavy armor, as the gamble of looking for soft spots against well-armored individual using a sword is not too practical, especially in the heat of battle. A decent dent on the armor can cause grievous injuries, as well as the shock of the impact. Those weapons can also work against anyone, but they're a lot better against armor.
- Swords are the best up close, especially indoors or in the middle of a big battle, once they drop the pikes as the enemy are within your sword's reach. These are offhand weapons that are carried by nearly everyone (sans those who are unskilled that are assigned to one weapon type). Takes more effort against well-armored knights, but they aren't too many, given the price of having heavy armor.
- Bows are the best option at long ranges during that era, bar none. Types of bow depends on usage and distance: longbows are better at longer ranges, the cheapest, but also the bow that takes more skill to use; crossbows are compact, easy to use, but lacks the drawing power and range, and it costs a little more than longbows, so it's best used at closer ranges; Arbalest may be heavier, not as compact, and costs a bit more, but it's the most powerful, as it can penetrate even heavy armor - but it's illegal to use against fellow Christians.
- Big two handed swords are rare, and their accurate use is debatable. They may not exceed 7 lbs in weight and may be around 5ft long, but they can only wielded properly by those who are big and strong enough to wield them like a regular sword. Said to be used by swiss mercs to break pike formations and to counter polearms, but will leave at that and let the others take over the charge once the pike formation had been damaged enough to leave a gap in the defense.
Anyway, Rapiers had only been coming round during the Renaissance era, but it's a civilian weapon used during duels and city conflicts during peacetime years. No army at the time would seriously consider deploying an army of fencers, and George Silver (Look him up if you're interested with all this in a realistic level. Oh and look up ARMA as well.) can attest to that (I read somewhere that he frickin' challenged an Italian fencing master to a duel, but it didn't look good for that Italian master after seeing Silver using a longsword and wearing decent armor, good ol' medieval style over pansy civilian fencing).
A regular longsword had always been better than rapiers, due to the ability to both slash and thrust, as well as the psychological effect its wounds can give (while someone stabbed at certain places with a rapier can still fight back). Medieval swords are actually pretty light and well-balanced anyway, unlike those "sword-like clubs" being sold to you by renaissance fairs and replica sword makers who uses "stainless steels", which are all heavy, ill-balacned and unwieldy.
Sabers are better swords and offhand weapons during the renaissance era, which by then, muskets and halberds are the name of the game.
A well equipped soldier would have a bow handy at long ranges, pike and shield when the charge is incoming, spear once the pike formation is broken, sword and shield (or if armored well, sword and bucker) once everyone is close enough), and a dagger if an enemy loses balance or is wrestled to the ground (they also had forms of wrestling as martial art). They'd have leather inside chainmail, and depending on social status, certain levels of scale and plate armor.
Personally, I train martial arts, and although not necessarily weapon martial arts, I practice a lot on the wooden sword, so if I were to think of a practical loadout for me: scale armor, halberd, offhand sword (not longsword), and an optional crossbow and bolts.