sword battles

well very true.. also the spearman knows he's screwed if opponent closes the distance.. so his tactic was probably thrust and backup..over and over again

I see two rapiers somehow as two spears, and for close fight I'll have four long pointy quillons then. 

Agreed. Plus if you got a nimble off hand weapon, you are pretty much in the clear even if they somehow do get beyond what you can control

Your sabers looked a little weak, so I corrected the image for you.  You're welcome. 

OK, more seriously and nitpickingly (because I have time to kill and and it really is more fun that way)...

Most of the terminology here is clearly from games, and doesn't really work in real life.

What exactly do you mean by "leather armor"? Rawhide scales or lamellar? Larger plates of rhino or elephant hide? Cooked and molded, or multilayered, or padded, or what?

IRL, "mail" is not a generic term for metal armour, but specifically means a mesh of interwoven rings. So "chainmail" is a tautology - you might as well say "chainchain" or "mailmail". It's just mail (or maille, if you'd like; sometimes it's useful to be able to distinguish it from the postal service). And what's "platemail" - just plate armour? A coat-of-plates worn over mail? Some type of so-called transitional harness, or Middle-Eastern "mirror armour", combining elements of both mail and solid plates?

And all of those are just armor materials. In practice a far more relevant question is what kind of coverage are we talking about here - just body armor? Half armour? Three-quarters? Full harness? Open or closed helmets? Hand protection?

"Longsword" and "hand-and-a-half sword" are the exact same thing. D&D used to get this consistently wrong, although IIRC they've finally gotten the clue in 5th Edition. IRL the long one-handed sword is just a one-handed sword, although more narrow terms like arming sword, saber or rapier exist for specific types (and a "short sword" is literally just any shorter-than-average short sword, from gladius to wakizashi, unless we're talking about George Silver who specifically uses "short sword" to denote a one-handed sword as distinct from the hand-and-a-half "long sword").

All kinds of shields were made of wood - are we talking about a large-ish buckler or Scots target, an intermediate viking age round shield or knightly heater, a large kite shield or pavise, 15th Century spiked and hooked six-foot dueling shields, or what?

Given all this vagueness, I'll just take it as license for a bit of creative liberty in making my choices.

I would assume that by "leather", "chainmail" and "platemail" you actually mean light, medium and heavy armour, as they're commonly used in video games and old RPGs. Now, IRL armour that cannot withstand the common weapons of its day is outright useless, so all the popular materials and constructions actually provide functionally similar levels of protection, and the actual difference between light and heavy armour is not what it's made of, or by what methods, but how much of you it covers. So I'm going to interpret leather as just body armour (akin to Fiore dei Liberi's "combat with sharp swords in a gambeson and... a pair of chamois gloves"), chainmail as including an open helmet and partial protection for the limbs (like a long mail coat with sleeves, or a cuirass with pauldrons and cannons for the arms and faulds and tassets for the thighs), and platemail as fully enclosing the person (be it a Maciejowski style tailored suit of mail with a great helm, or an actual full plate harness).

Now, for the actual fights...

So to put this in some kind of concrete context, let's actually say that I am the late 14th Century martial arts instructor Fiore dei Liberi, challenged by a rival master-at-arms to a duel with live weapons and minimal protection - and then the base villain shows up for the fight packing distinctly not-agreed-upon gear! He jumps me before I have time to protest so, loath to just run away, I quickly grab something from the weapon racks and make the best of a bad situation. What do I go for?

Opponent 1: leather armor, shield and spear (wstalcup would choose to fight him with a shield and longsword)

Ah, this one doesn't cheat. I like him! We're similarly armored in soft leather gloves and gambesons (quilted jackets of very densely padded or multilayered cloth, much like modern kendo armor, that cover us from thigh to neck). We can even say the gambesons have an outer shell of thin leather, to kind of keep with the original premise, although the leather doesn't actually provide any protective value here, it just looks stylish and adds a bit of weatherproofing. I could pick shield and spear, myself, were I feeling particularly sporting today, but I think personally I'd be more comfortable with shield and sword. The shield, probably a heater or round targe just large enough to cover me from hip to shoulder and with straps set up for holding it in a variety of ways, mitigates most of the spear's reach advantage, allowing me to close in and work at the optimal distance for my sword, most likely a handy Type XV or XVIII very much like many of those found in the famous "Castillon hoard" (a large military shipment of used swords, sunk in and recovered from the Dordogne River) - a "longsword" in old D&D terms, but IRL an "arming sword" or "riding sword" or just "sword". In any case, this would actually be a fair fight. Nice!

Opponent 2: platemail, longsword and shield (wstalcup would choose a flail and mace)

Oh, you cheeky, cheating jackass. Coming in full armour after calling for a lightly armoured encounter? What a conniving coward, an absolute spineless poltroon. I give him the fig and do the best I can with shield, mace and the dagger that I assume was omitted from the list only because everybody should already have one on them, anyway. The mace is somewhat shorter than his sword (again, I take that "longsword" is meant in the D&D sense and that he's using a regular knightly one-handed sword), but it's designed for dealing with armor and the shield again mitigates his reach advantage. The general plan would be to get up close, bash him in the head with the mace to buy me time to get even closer and then wrestle him down to the ground, drop the mace and shove my dagger in through one of the relatively unprotected openings in his armour like the helmet visor or eyeslits, the armpits or the groin. Not nice, at all, but I'm at a big disadvantage and he really is asking for it, the twit.

Opponent 3: chainmail, 2 handed sword (wstalcup would choose buckler and rapier)

Still cheating, but not as flagrant... maybe he's an out-of-work mercenary and the great sword and an old hauberk are simply all he's got at the moment? I suppose we can indulge him. In any case, you do not want a rapier for an armoured fight of any kind (and besides, as a late 14th Century fencing master, I've never even heard of such a thing, anyway). I'll take a heavy longsword (AKA "bastard sword" in older D&D), meaning a literally longer-than-usual sword set up primarily for two-handed use, most likely a Type XVII, or some other kind of two-handed estoc, because they're specifically designed for dealing with armor, with enough heft to knock tin cans about and a narrow but sturdy point to be driven in through the openings between plates or even split mail links apart. Of course I still - and always! - have that dagger at my belt, just as a matter of everyday casual duh. But, remember, I am Fiore, damnit, best known to history for my work on longsword fencing! This won't be an exactly even match, but I can live with it; maybe literally, maybe not, we'll just have to see.

Opponent 4: leather armor, dual 1 handed axes (wstalcup would choose buckler and spear)

Well, there's a funny sort of fellow. What's the point? Is he a performer of some kind? A half-crazed wild woodsman? I could just keep my distance and poke him in the eye with a pike or long spear... but honestly I feel like we should give the poor fellow a proper fight, as I do kinda sympathize with a man who would put his life on the line for a silly thing like that. So, I'll go with the good old sword and buckler; same sword as in encounter 1. It's an honest enough contest, I suppose, but I think he'll lose because I have not only a reach advantage but also more viable options at any given distance, even up close. I'll do my best to be nice and not hurt him too badly, though, as I'd rather like to chat over a pint of beer afterwards.

Opponent 5: chainmail, shield and flail (wstalcup would choose hand and half sword)

Not sure why he'd bring a flail, given that I'm only wearing partial "soft" armor... but I guess that's his private business! Again, dirty cheating bastich with the excessive armour, but if we really must I'll take him on with buckler, spear and sword (and dagger!), a popular armoured dueling combo judging by period treatises. The buckler provides protection for my lead hand, which is otherwise notoriously vulnerable when using a spear two-handed, while the spear - I'd want a somewhat heavy one, or rather a pollaxe if I had my choice but it was not on the list - lets me poke at his unarmoured face and lower legs from a distance, and he'll have a hard time covering them both with his shield. If he gets up close and personal, I'll drop the spear and go on with sword and buckler; he does not want to get too close, though, because his flail becomes very inefficient inside its optimum reach (far more so than a spear). His heavier protection does give him a significant advantage, but nothing that couldn't be overcome with superior skill and control, and again I'm not inclined to play nice at all.