At lower levels, your melee weapons are a crapshoot. You can buy stuff off the AH, you can wait for a random world drop, an instance drop, or you can get the occasional quest reward. Once you hit the outlands and get to 70 and such, a 2H weapon is almost always better. 1H are a better option than they were with the +20 Agi, but you'd still have to fight to get 2 that match the stats of a 2H. For instance, I think an actual good option for a 1H would be Spiteblade, which drops off of Netherspite in Kara, but from what I hear it has a relatively low drop rate, and when it does drop, how are you going to look rolling on it against a rogue? Or a DW warrior? I took the DPS spreadsheet from TKA Something (I think) and calculated a few 1H combinations vs. my current weapon (Blackened Spear from Thrallmar rep), and while I don't remember how those ranked, I know that the 1H weapons from arena, with +20 agi, would theoretically give me the same DPS as my weapon.
So DW is possible, but I think getting a 2H is just easier, and you don't have to fight as much for it.
As far as type of weapon, I really don't think that matters. You'll hardly ever find a sword that has stats you want, so axes and polearms are usually the way to go. I had the crystalforged axe for a while, until I got my blackened spear. The sonic spear has refused to drop for me, so I gave up on that. As for raiding, Kara has legacy, of course (an axe), but I really don't think that's an enormous improvement over the blackened spear - except for the stamina. It is an improvement, though, so I'd gladly take it. Zul'Aman will have a 2H axe - Trollbane - that looks nice, but I don't know if I'll ever be able to get it. It's one of the timed rewards, and I don't know that my guild is serious enough to ever get good enough to get those timed rewards.