Short version:
For the bottles I hand wash, dishwasher sanitize and then they go into the box upside down until I need them. Out of the box and chemical sanitized prior to immediate use.
Longer version:
Bottling... the portion I hate the most and an unexpected benefit results. Since I hate bottling I tend to leave in my carboys longer and before bottling I may have some very fine sediment that has finally dropped all the way out. At that point, I'll rack again to another container with some K-Meta and leave that last final bit of crud behind; I like a very clear mead.
For myself after I have cleaned and scrubbed bottles, I put them through my dishwashers sanitize routine and then they go into their box upside down until I am ready to use (usually weeks later). When I am ready to bottle, I mix up fresh Star San, let the bottles sit in the bucket for 2-3 minutes and then they go into my plastic tray that holds the bottles upside down. Once I have them all sanitized then I start the bottling process.
I dislike the bottling wands as I feel like I need a 3rd hand when starting. To help with that portion I glued a cardboard 4-pack holder down to a piece of wood and the bottles go in there. This keeps the bottles from tipping while I am bottling.
I have a few carboys that have a spigot and I'll sometimes just put some hose on the spigot and open it up to fill the bottles without a bottling wand.
With either of the above methods I add CO2 to the bottles before bottling so I can minimize O2 in this process.
I eventually tired of bottling like this and I also wanted to force carbonate and I moved to using some kegs. I added a bottling gun and will bottle out of the kegs and while you have to clean and sanitize before and after, I am much happier bottling this way.
If I have a mead in a keg that went in not quite as clear as I would have liked, I put it into a keg with a floating dip tube so it dispenses from the top of the keg and I get the clearest mead I can until I hit near the bottom.
