Drop the helmet down to a kettle hat, that'll save you about 4k. I'd suggest going with leather gloves too, 1k more for 2 armor isn't worth it if your going for budget.
My go-to economy weapon for polearm has been the hafted blade, it functions a lot like the bec does, and costs about 5k. just does cut instead of pierce. I'm pretty sure it would be a easy transition from a poleaxe to the hafted blade for ya. The long voulge (4k) is a fun weapon to use too, it has such long range it makes for a good anti-cav and support weapon.
If you play siege, grab a quarter staff (1k) and always spawn with a siege ladder (ladders have no repair costs). You'll be helpful to your team, and can scavenge better polearms during the match without leaving yourself defenseless.
