Been leveling an Arms (Poleaxe spec) warrior the past few weeks, now to lvl 48. This build favors slow axes or polearms with high white damage & lots of crits. Note that I mainly do quests & instances, and very little BGs.
At 10 to 20, just get the best green that suits your style. You will be competing with lvl 19 twinks for blues, so they are often ridiculously priced at AH. I enjoyed using Gargoyle's Bite with Fiery on it from lvl 20 on. That combo just wiped out mobs in this range.
There's no debate that the Whirlwind weapons are fantastic 2 handers in the 30s, and a relatively easy quest reward to get with a bit of help from a higher level friend. For Arms, the WW axe is just outstanding. Lasted me from 32 to 44, again with a Fiery enchant. At 43, I was searching for an Executioner's Cleaver on the AH, which has excellent stats for Arms (high white damage, with Str & +Hit). It was never available, but I found a Kang (lvl 44) relatively "cheap" (150G, usually 225G or more on my server). I spent the cash & never regretted it. Although it doesn't have traditional Str, Agi or Stam stats, the Rend procs quite often for 56 dmg every three seconds to a total of 560. Remember that each individual Fiery proc gives you only 40 dmg, 60 with a crit. At 44, with mainly blue gear and no enchant on the axe, I was mowing down 49s with Kang without difficulty.
From prior experience with a Ret Pally, Ice Barbed Spear is certainly next on my list (also slow, with great stats). That will take me from 51 (assuming I actually win an AV) until Outlands instance drops, or even some Outlands greens. Thrallmar War Hammer (lvl 61) for a 2H mace user comes to mind. If you favor 2H swords, consider the combination of Truesilver Champion (crafted), which quite often pops a shield that you can fight through, with a Fiery enchant at level 47. The Tusker swords are also slow, heavy hitters in the mid 40s, if the blues are out of your price range.
For Tanking at lower levels I went with whatever blue quest rewards or AH deals I could find, like Diamond Hammer, Looming Gavel, Wingblade and Outlaw Sabre. Dual wielding these at this level is fun too. In mid 30s I picked up a Steelclaw Reaver, which had good speed (builds aggro fast & nice not to have to wait for the next "on hit" ability to go off) & worked quite well with axe spec. Used it right to 48, and just switched to Axe of Rin'ji, also a fast axe. Peformed really well in a ZF run last night.
If you're keeping a weapon for 10 or 12 levels, it's worth getting an enchant on it. I feel that Fiery is the most cost effective for the slow weapons at low to mid levels (40 dmg proc is obviously a bigger deal in the 20s than in the 60s). I have been putting Greater Striking (+4dmg) on my 1H tanking weapon, since the damage on each hit does better over time & holds more aggro than random procs. There is also a huge price jump to +5dmg, which I don't feel is worthwhile.
Remember that at around lvl 60 Outlands greens are much cheaper and often outperform pre-expansion lvl 60 blues, or even epic BG rewards. I only used the Immovable Object (shield) for a few levels when I found a better green for my Pally. Shop carefully.