Ulak & Claws, Knuckles, Handwarps, Martial Staff, Martial Sword, Bladed Staff, and Shuriken.

The skills posted by Ninbei are Weapon Specialisation skills, which max relatively easily. Another thing to take into consideration are the bonuses each weapon type generally has:
- Martial Staff, Bladed Staff: Double critical damage
- Ulaks/Claws, Knuckles, Handwraps: 5% extra critical chance
- Martial Sword: parry bonus
- Shuriken: it's ranged and that's basically it.

So, IMO:
-  it's no use to max more than 1 of the Staff skills
-  it's no use maxing Martial Sword (since the damage will be lower due to them granting a parry bonus)
-  it's no use maxing Shuriken, since I don't tend to throwa lot of them, even when designated puller.

Then for Weapon Skills themselves (determining whether you hit the mob), there's the following. In parentheses you'll find the weapons that use them.
- Two-hand Piercing (Bladed Staffs)
- Two-hand Slashing (Martial Swords)
- Two-hand Blunt (Martial Staffs)
- Thrown (Shuriken)
- Hand-to-Hand (Ulaks, Claws, Knuckles and Handwraps)

I agree with Dythan.  Max martial sword.  Tranquility from the arena is a great weapon and is extremely useful if you end up being the tank for the group or if you are soloing.

Then it just depends on what you use.  Fortunately it's not that hard to get those weapon skills up so if you get a new one that's better just raise those skills.