Cast iron grates .... work on building up a good seasoning on them, sorta like an old fashioned cast iron frying pan. Since the first pre-use burn for mine, the only cleaning I've done is to scrape them down after the grill has cooled a bit. The grill brush I have has an angled section of the scraper part that matches the sides of the grate rods. Does a good job of scraping those bits that cling there. After scraping/brushing, I lightly oil the grates.
Then, when I cook again, I give the grates one more light brushing after they're hot again. The heat kills any beasties so I don't worry them being clean from a health/sanitary standpoint. When ready to cook, I dampen a paper towel with cooking oil and oil the grates. Use tongs to apply the oil. Don't put enough oil on the towel for it to be dripping. A light coat of oil is all that's needed. Note: the more seasoned the grates become, the less oil is needed for the cook. In time, the grates will become like a non-stick frying pan.
Re- stainless steel grills.... A new SS grill is like a brand new pickup truck. (BTW, congratulations to both posters! ) Dread the day that something dings the truck bed. Work hard to prevent any scratches. But after a while, something will scuff the paint. Worry lessens a bit. Then scratch #2 happens. "Oh, heck, I bought this truck to use it." After a while, those small dings and scratches don't matter any more. Then, the real enjoyment of the truck begins, as it's used for what it was designed to do.
Same with a SS grill. It's beautfiful right out of the box. Looks too pretty to use! But, as with the truck, you bought it to use it.
Heat will affect the color and shine. A well seasoned grill cooks better than one right out of the box. Sounds like the brown color is just the beginning of accumulating a layer of carbon on the grates. IMHO, that's what you want to happen. As you acquire a coating of pure carbon you're actually cooking on a non-stick coating. So, don't apply a lot of elbow grease to remove a protective and otherwise beneficial coating on your grates. Don't worry about those grill equivalents to a scratch in your pickup bed. Instead keep your thoughts on those great meals your well seasoned grill will provide.
Just my 2-cents this morning.