Whats the best questline for a swordsman using the one-handed skill. I'd like to be able to get some good swords I'm a traveling swordsman such as that of Mugen from Samurai Champloo. I use light armor and a blades sword

Best sword you'll find is a sidequest in the Thieves Guild. I'd wait until you're in the 40's to do that though, it's a leveled weapon. Same goes for dragonbane. 3rd coolest third is best done around 20-30ish, for the daedric lord meridia. edit: Another cool sword for early levels is the Ghostblade.

There really isn't a best questline. The Companions would make the most sense as they are warriors... Alternatively either side in the civil war should work

Meridia's Sword is great!, there are better ones, but the Kill-Undead Effect is awesome

Okay what about a quest for cool light armor? I don't know why I decided to join the imperials I just thought they'd pay better I guess..

Not really. You can craft it all yourself, or alternatively find it on random people walking around.