If it's just mild steel and thin wall, I might look at one inch... is this the part that the seat will bolt to and be attached to the floor? You could do 1/2" but it would need to be more than a simple square, you know, re-enforced at the corners with some triangles or something.
I understand trying to keep it light and simple but it wouldn't hurt to go just a
little beefy in this area...
