On a related topic.
Now when Dawnguard is out, isn't it worth it to get Dragon Armor perk for the new weapons?
2H does more Damage Per Strike, while 1H does more Damage Per Second, all else bing equal. The discrepancy is widest at the beginning, and narrows as you max out your Smithing. Also, a Shield adds a whole lot of perks that are handy in, and of themselves. You can Bash with a 2H effectively, it even does more damage, but protects only against Melee, and can't be used with the left (Shield) side of the Block tree. You can also combine 1H with a spell, or other weapon for a lot more versatility, and Perks to compensate.
In a nutshell, 2H is simpler, but more limited because of it. If you're Smithing, especially Heavy side for the best weapons, the difference in damage is minor. I'd go 1H with a 1st timer, so you can sample all that the system has to offer, and pick out what you like. Block/Bash, Spell/Blade, Dual Wield, even Shieldmage, and other weird combos. That's the thing, 1H can be combined with whatever's in the other hand, 2H can't.
Armsman is more damage. Bladesman isn't worthless, but unless you build a character around it, it's generally accepted to be worth <three perk points. I think of the 3, Hack&Slash is the most useful, you can stack it with the Targe of the Blooded, Fire Afterburn, and/or Lingering Poison to counter Regeneration, or keep them dying while you block, or circle around for another charge. A Handaxe of Burning with Hack&Slash(3) is actually a decent amount of Damage over Time (AKA DoT) especially at lower levels. Unfortunately, you have to find one, as none are scripted to be just lying around. All 3 weapon specific perks (or 6 counting the 2H versions) are calculated from the Base Damage, so Iron does the least, and Daedric/Dragonbone the most. (I've heard it's a total of 15 per strike, for H&S.)I read that Bladesman is WORTHLESS.
Armsman is good?
As Streets said it, in term of Effectiveness, the difference between Steel Weapon and other weapon is not very important at the end, IF you have high Smithing, Alchemy and Enchanting.
pms00 has a nice video on this, to show that the difference will be just a matter of taste and esthetics more than effectiveness.