Hi Max!

I will show you how to use each word appropriately in the sentence you chose:

"meet":

I would like to become a part of your team because my qualifications and work experience fully meet your requirements. 
 

"fit":
I would like to become a part of your team because my qualifications and work experience fit the requirements.
 
"suit":

I would like to become a part of your team because my qualifications and work experience are suited to your requirements.

"appropriate":

I would like to become a part of your team because my qualifications and work experience are appropriate for the requirements.

----

The differences between the first three -- meet, fit, and suit -- are more a matter of style than anything else. I tried to choose the phrasing according to what sounds most natural to me.

The words "fit" and "meet" are interchangeable as I have written them (so you could still say "fit your" or "meet the" and it won't sound too awkward), but "suit" is a bit more awkward sounding in the sentence you chose unless written as I have shown.

The word "appropriate" as it relates to the other words (fit, meet, suit) is actually an adjective.

If used as a verb (example: "I will appropriate the money."), "appropriate" means 'to take', usually without permission.