I would use 1/4" mild steel depending on the size of the grill (A36 or something similar). But if you are just making one, it may be most economical to take whatever is available. I have machined fire grates and cooking grates out of this material that span a 16" to 18" opening and they work just fine. I'll be making a grill similar to what you are considering sometime in the future.
Sheet metal won't do it, even if you support it. It will warp.
You could use stainless if you are a cleanliness freak. Much more expensive though.