Upkeep doesn't increase as the weapons get more expensive after heirlooming.
Anyway, here's my list:
All-round:
Knightly arming sword. Decent cut damage, decent thrust damage, good range, decent speed and can be used quite well from horseback.
Fast/spam:
Steel pick. High damage, high speed. Very short. Good for agility builds.
Niuweidao. High slash damage, high speed, cheap and 88 range.
Slow/high dps:
Military cleaver or Iron war axe. Cleaver with 35 damage and the axe with 37 damage on the swing. The cleaver has decent range, but the shorter axe makes up for that with shield busting ability.
Anyway, there's a lot of options and it depends on your build. If you want to make it hard on yourself, take a short weapon with a strength build.