I am walking around with the walking stick right now and I am a melee character. My team mate suggested that I get the Shillelagh because it is classified as a staff. I disagree with that because it does not say it is a staff. Any help will be appreciated, our overlord has deemed it a club type of weapon what do you think? The reason for this for the melee person to use fire pact.

Since "Staff" is not an official classification described in the rulebook, I think that only cards with the word "staff" in the name count. Which means neither the Walking Stick nor the Shillelagh count.

All the items with "staff" in the name are magic weapons.