I use Star San at home for most things. I also autoclave a lot of stuff at work the day before I do a brew. For cleaning I use the PBW cleaner. I don't sanitize as much stuff as most people, as I have access to sterile, individually wrapped large pipettes (in place of a beer thief, of example), flasks, etc.
I think people are a little nuts on most brewing sites as far as sanitation goes. I watch the videos where people sanitize all their stuff, then stick their arm down inside the fermenter, or let their lid touch the floor without re-santizing. The sterile technique I have seen in most brewing videos is pretty poor. A good example is people talking about sanitizing their bottling wands for 15 minutes, then leaving their bottling bucket open to the air for 20 minutes of bottle filling, while the end of the wand rests on their kitchen floor. Why did you sanitize all the stuff again? Anyway, I follow the instructions for sanitizing my cleaned equipment, then I use it. I doubt a freshly boiled wort with hundreds of billions of healthy yeast has much to worry about in terms of contamination. I guess the fact that most people don't have contamination problems tells you brewing is a pretty robust process. Heck, those Belgian monks were doing it in a musty church basement with zero knowledge that yeast even existed, let alone bacteria.
I usually store my stuff cleaned and dry, I rinse it once with water, then I sanitize and use it.
Yeah, I use Barkeepers friend for cleaning. StarSan for sanitizing. And it's the stuff like you mention that has me wondering what others do. I found myself, during the process, having to continually lay something down, then re-sanitize it. Having D-girl around for the extra set of hands is nice. But then I also wonder 'How long is this fermenter good out in the open air after sanitized and drained before it needs sanitized again? It's very much like cooking a multi-course meal in having to plan everything so all the pieces are ready and come together when you need them.
I don't worry too much about pre-boil, since everything will be killed by the heat. But there in the last 15 minutes+ you need to put the wort chiller in the boil to sanitize it, make sure your yeast is ready, sanitize your fermenter one last time, put a lid on it if you can (sanitize the lid), sanitize any strainers or tubes or other wort transferring tools, make sure you late addition hops are ready and measured out, etc.
My method has been to have one of those 6 gallon buckets filled with StarSan. At the beginning of the brew day everything small that can fit goes in it (airlocks, bungs, tubes/hoses, strainer, spoon, measuring cups, etc.). Then there's a spray bottle of StarSan sitting around to get other things with. The fermenter is clean and covered, maybe sprayed with sanitizer, but not "officially" sanitized yet. There's hardly anything I need that I can't fit in the bucket, and then I can just pull it out, shake it off, and it's ready to use in under 30 seconds. I think my next brew I'll set out a piece of aluminum foil and spray it down with sanitizer, using it as a surface to set things momentarily that I don't want to put back in the bucket and have to rinse again. I can just set them down then spray them over with the bottle for the short time that they're not being used. So after the boil, as the wort is chilling, as I need things I just grab them from the sanitizer bucket. After I sanitize the fermenter I also sanitize a bung or lid and put that in place to keep as much air out as I can until the wort will get splashed in.
So I think I'm doing alright in that respect. But after it's all said and done, I'm not really sure what to do with the equipment. I have that swamp cooler bin that I can fit the plastic buckets and just about everything else in. I'll likely just store it all in there between brews. But I can't fit my carboy in there as well. How do you guys store your carboys? I was thinking if I put a bung in there it won't air out and that could be bad. If I don't put a bung in, air and bacteria can get it. Things are sold where you can store them upside down on a holder. I guess that's about ideal. But I don't have a dedicated brew room or shed. I'd rather pack this stuff away for the few weeks between brew days.
I'm probably just over thinking it. I should probably just let what may happen to it in between and just worry about cleaning it extra well before each use. But if I can take an extra 2 minutes to make my life easier down the road and require less cleaning, that's something I'd like to do.