Any upgrading should have a "goal".

What do you want to accomplish that the existing bike doesn't accomplish?

"Coolness" is certainly a viable factor. Yet, you also have to research the parts to see if they fit your needs. Are the cranks you've chosen 2-speed cranks? Nothing in your description mentioned wanting multi-speed.

If you are wanting a new chainring, then look at the specs of the crank. Does it use the standard 110mm or 130mm bolt circle? 5 bolts?

Then choose the number of teeth.

I don't ride fixed, but I'd certainly consider some of the "drop-stop" rings of various designs.