The Mace would be me weapon of choice if it came to picking "one" weapon against all facets of middle ages combat.
A mace was simple enough and good enough that it could be used against unarmored and armored enemies, it would crush plate armor so it was a good all around choice that worked against most varieties of armor. Though you'd be at a disadvantage vs say, someone with a spear.
A sword is not going to do much vs someone wearing plate. That is why they had to use half-swording techniques when fighting against someone in plate. This means you hold the sword more like a spear, putting one hand on the blade above the hilt and using it like a spear. The goal would be to slide the sword into a weak point where the plate armor isn't protecting you, like the neck, arm pits, groin, or helmet visor or to use the pommel to strike against the plate and stun them. This technique also made use of trips/disarms as well, basically anything that would make it easier to get your opponent down and slide the blade into a weak point.
In my other hand I would like to have a buckler. The buckler different from most shields in the fact that it was held in your palm with a handle, it wasn't strapped to your arm like larger shields were. On top of this bucklers would be quite varied and customizable. You could have things like serrated edges on the boss of the buckler (which could be used to cut your enemy), a spike (which could damage their weapons or used to hit them with), even a latch which could be useful to trap their weapon and disarm them.
Since they were simply grasped in your hand that meant if your it got held or "pulled" by your opponent you could simply let go of it, whereas a guy with a shield strapped to his arm is stuck to it and could be thrown off balance or pulled to the ground/trapped.
Bucklers are often overlooked when it comes to media (movies, games, etc) and treated as the lowest "class" of a shield, but in truth they were one of the most used and even outlasted the use of the larger types of shields. Hell they even found one in the Jamestown settlement.
When it comes to armor choice, I'd go with plate hands down. There's a reason it was expensive, because it offered so much protection. Arrows/swords? Near useless against plate. The main weakness was crushing/cleaving weapons, like the war pick, mace, or axe.
