I've had a few cast iron pans and a carbon steel pan for a few years now. I just wash them with dawn dish detergent (make sure whatever soap/detergent you use doesn't contain lye) and a sponge until all the food bits are gone and the water cleanly skids off the pan. After, I shake the water off and hand dry with a cotton dish towel. I don't put oil on them unless I'm gonna store them for months at a time.
You mentioned your pans are new so the water may not slide off like a well used and seasoned pan so just scrub and rinse until the food bits are off. If there are any difficult bits, you could buy a plastic dish scraper or just gently scrape at it with a metal spoon. Don't worry too much about damaging the pan when washing; cast iron has lasted many families many decades of cooking and abuse.
Just make sure not to drop it or heat/cool it too quickly and it'll be fine
Still surprised it's worth $200. I thought it'd be worth a few cents or maybe a few dollars at most