Warrior leveling is only painful from level 8-15 or so. If you can get to level 20 without ragequitting the class, you'll be fine. Also, you'll want to ALWAYS be fighting mobs that are equal level or lower. If you try to fight mobs that are 2-4 levels higher than you, you're going to have a bad time.
Yes, go 2-handed fury; it's much better than Arms for soloing. At 40, you can respec Arms for Mortal Strike, but Fury is still better IIRC.
Always use blue weapons, and keep them updated every 5-6 levels. For example:
Searing Blade(18) ->
Gizmotron Megachopper(24) ->
Whirlwind Axe(30)And the axe will last you until 40-42 or so, and from there you've got a lot of weapon choices to go from; like the SM quest axe, or Executioner's Cleaver, or Rockpounder, until you can get Ice Barbed Spear at 51, which will last you to 60.
From 20-30, you can also dual-wield. Yeah, yeah, people will say "no, don't dual wield, the miss chance is too high", but I leveled 22-30 with dual-wield and was just fine. Yeah, there were frequent misses, but when you're attacking that quickly with two weapons, misses don't feel as bad as they do with 2-handers. I compared a level 21 2h and level 21/24 dual wield, and found them to be roughly the same killing speed.