Materials seem to matter sometimes. For thaumaturgy, the construction of the circle seems to matter primarily for convenience and focus in various ways. Chalk serves Harry well for most of his spells, but I doubt he would even consider using chalk for something on a larger scale, like interacting with Little Chicago. Refining the circle in various ways helps the wizard build the magical construct and keep it solid. When the exact form of the construct matters in a big way (like, say, containing ) then you'll want as much help as you can get to build the construct.

There seems to be a point where magical creatures can break free of circles as well, since Harry seemed to struggle to keep the Erlking in his circle way back when.

Of course, that's mostly just making declarations to tag for your higher-level thaumaturgy spells. So I'd say the spraypaint idea would work well for anything quick and dirty, but you'll want to start refining that in various ways to get your tags for stronger spells.

I actually love the idea of a wizard graffiti artist refining his circle by making his art more and more complex.