All data is based on the New World Preview Client and will change before release!
The Straight Sword is currently the only weapon that allows you to use a Shield with it. Its first skill tree is called "Swordmaster" and has mostly sword-focused offensive skills, while the "Defender" tree is focused on defensive and tanking abilities. Some Sword abilities allow you to taunt monsters in PvE in order to manage aggro in groups.
Swords benefit primarily from Strength, but Dexterity also contributes.