Right, we started by cooking meat with a stick over a fire... no dishes to clean, no greasy spills, the fire burnt up any potential mess. It's the opposite with ceramic cook tops, any spilled water, spaghetti sauce or bacon grease will just keep calcifying and carbonizing. But of all modern cooking options they can stay the cleanest! Also, you avoid the health and environmental hazards of natural gas.
The trick is to clean as you go. Never lived with anyone who subscribed to that. Maybe it was my Boy Scout training. When you do cook over a fire you need to prepare carefully (ever soap the outside of a pot to make it possible to clean off the soot?) and clean up plates and pots while the food is still moist. Throw everything in the sink and everything just gets dirtier. Plus, it only takes seconds to wash a cutting board and put it away before you go to the next cooking step... Anyhow, with ceramic cook-tops I pre-treat with Goo Gone: Oven Cleaner.
Wipe that residue up with a paper towel, then use a sponge and Weiman cleanser as in the image below. A moist dishrag is best at getting up the cleanser residue.
A BEFORE picture.