I personally prefer to use two-handed weapons for my Nord warrior characters. Besides the perk spread being more manageable since you do not have to split it between one-handed and/or blocking, it also looks better to have a large, deadly weapon strapped to your back!
You obviously can't go wrong either way! I personally play the same style every time (Nord warrior with 2-handed weapons as my major style of combat)
The Dragonbone great sword is definitely the end all in terms of most honorable. Only the mightiest of heroes should wield it! In my current playthtough, I plan on bringing a Nord Hero battleaxe into Sovngarde, then rewarding my character with the Dragonbone equivalent after he defeats Alduinto use for the rest of the game.
Anything other than elven or Daedric (including those of the Daedric Princes) will suffice. I prefer Iron, Steel, Nord Hero, and of course Dragonbone.
I have to go with Tae on this one. 1h or 2h is a personal choice. I would suggest anything that isn't Mer or Daedric in origin for a Nord. The top of the list for me would be Skyforge Steel, Nordic, Dragonbone, and Nord Hero. They all just have that whole heroic and honorable warrior vibe to them.
Dragonbone Battleaxe, mainly because:
1. Nords seem to like battleaxes the most. The highest damage ancient Nord weapon (discounting bows) is the battleaxe. Ysgramor's signature weapon was a battleaxe. Why he had a shield is beyond many people.
2. It's incredibly badass in a Nord way, with a modern twist and yet you also feel as though this weapon will have songs sung about it for ages after your time is over.
Another alternative would be the Ebony Battleaxe if you don't want to do smithing. Daedric is too evil looking and everything else looks kind of weird. Iron is good for low levels. If you want, you can also use the Headsman's Axe. It's dark and grim, like Skyrim itself and you yourself nearly died because of one.
Well, the question you ask yourself is can you go about hunting dear in the forest by swinging your battle axe around? I don't think hunting and therefore the use of archery would be disapproved of. Take Aela, for example, she uses a bow. Now, when I play an honorable character, regardless of whether they're a Nord or not, I don't sneak, so the archery game becomes quite a bit different. Actually it becomes quite a bit more fun.