Modern material science vs medieval weapons

[Batman]

Watched Percy Jackson & The Olympians: The Lightning Thief tonight and, lo and behold, when we get to the demigod training camp...it's all swords and shields and leather armour.
Nevermind the degree to which those would be utterly useless against modern firearms, I just wondered-if the weapons you had to deal with were limited to swords, spears, arrows etc-the standard medieval/fantasy arrangement-what would be the best modern material to use, or the best combination of modern materials? I know for metal armour the obvious answer is titanium, which can do everything steel does only better (if you can afford and have the means to shape it), and I know that kevlar isn't so hot against piercing weapons, given it's a fabric, but what about, I dunno, carbon composites? Fiberglass? Ordinary modern plastics?
And by all means, if any of those ideas are totally ridiculous, feel free to mock me for it-as long as you explain to me why that is the case.

[Josh]

More parameters? I mean, we're talking... melee weapons only, no powering elements (gunpowder, electricity, etc?)

I mean I'd totally take the taser to the swordfight, given that any half-ass swordsman would fillet me no matter how fancy a metal I'm packing on a blade.

But if you're limited to non-powered materials, I'd guess those newfangled ballistic inserts and so on would be whizzer. What would really kick ass modern-material-wise in an antiquated setting would be the ranged weapons. Modern bows and crossbows and folks who know how to use 'em would be sick sick sick scary.

[Batman]

I was mainly thinking about armouring up against people with swords, axes and such. And frankly even real-world leather armour is bound to make your tazer moderately useless given real world heavy clothing can.
And yes, of course, modern day iterations of bows and crossbows (and probably slings) would be game-turners. But then, we're back to 'why not use guns'. Which can do the same much better, with much less need for training, with the only real advantage the bow/crossbow/sling having being they're reasonably silent by default.