swords

One-handed swords, whether for use in combination with a shield, as you suggest, or for combat on horseback. Celtic and Germanic swords were one-handed during that period; so was the Roman spatha and its "heirs" (a spatha is longer than a gladius, it is better designed for combat on horseback as well as one-on-one on foot combat, contrary to the gladius which was used in combination with the spear in shield-wall formation; there is little use for a longer reach when you're in direct contact with the enemy shiedwall; either you need reach to stab above the shields, and the spear is much better than any sword; or you need something with which to stab quickly between small openings, or to hamstring foes below the shield, and in that case the gladius is fast, handy, and easy to retrieve -- hardly any hilt-piece that might get stuck on the shield's rims when you draw it back).
Bastard swords and two-handed swords developed later, as armour developed (and thickened) as well. Basically, when your foe isn't wearing full-plate armour, you don't need so much weight and brute force to hack through the layers of metal; you just need something quick to cut, backlash and stab -- mostly stab. The longer reach and heavier impact of two-handed swords would be counter-productive in that context. You don't need to cut a guy in two to kill him, just open him up enough, and faster than he can open you up. One-handed swords and shields do that very well. As for horseback, here again, too long a sword would be a problem: you don't want something too cumbersome that might end up injuring your own horse! Just something you can easily wield right and left, and mostly down, to hack down on men on foot.

"Occasionally I'm callous and strange."