I like to use a flaming burst greataxe on any trolls I might encounter to cut off there regen. EG: Stormcleave, Redwillow, Gwylans stand, etc. So you want one either lvl6 or lvl8.
After that at level10 I tend to stick with the carnifex unless I get lucky enough to have a greater bane at that lvl (usually I dont, so I have to wait until 12)
At 12 I have a nice line up
Greater orc bane - Feats or Famine is one of the best xp/min quests in the game at this level, and its all orcs. So this is one of my favoute lvling axes.
Greater Giant Bane - Madstone crater is nice xp, as well as Gianthold Tor, and Gianthold ruins in general.
Greater goblinoid bane - Similarly Cabal for one is nice xp, and all goblins.
Greater Undead - Generally zombie type undead are really quite easy, so if you can go for a blunt type one. Either maul or greatclub works fine since the multipler doesnt matter on undead (well for non-burst ones)
Greater Evil outsider, or just a good holy silver. This should serve you throught the higher levels (around 16+) until you can craft up a triple pos/mineral2.
Greater Dragon bane, if you start running the Dragon raid or Tor much before you manage to get your t3 greensteel, be sure to find one of these.