I have a 22.5 Weber, and other than keep the grate clean and lubricated, there's not much more that I do. Every once-in-a-while, I'll scrape out the build-up that gets in the lid and the bowl.
I've learned from my
WSM water bowl that the porcelain really holds up! I've actually used a stainless steel scrubby on it with no problem, although I do it somewhat gently. There are probably some folks that wouldn't advise this.
If the outside is dirty, you could use a scrubby (plastic, if you're nervous about it), and some dish detergent.
How dirty is it? You usually don't see any rust...or at least I've never seen any on mine. Not sure about the gas grill: I have one (not a Weber though), but it usually stays in the garage.
Happy cookin'!