That's kinda like asking what do you print signs on.
What is the flier for?
Does it mail... In an evp, tri fold self mailer?
Who is it for, who does it go to. If it is going to doctors advertising a new CAT scan facility you want it on nicer paper than if it is for the neighborhood kid advertising he will mow lawns.
Is it theme specific? Christmas red, Halloween orange, etc?
Will the copy be black? Color?
If you don't know what it is for then just put it on 11" wh. 20lb. It's the cheapest!