My recommendations:
Soak in Oxyclean overnight (I use a rectangular cooler). Run dishwasher if any dishes are in it.
Next morning, inspect each bottle for "funk" left in there and use bottle brush if necessary. Remove labels. Dump spent oxyclean. Remove clean dishes from dishwasher.
Fill cooler with sanitizer water and soak a few bottles at a time (along w/ caps). Use dishwasher racks to dry bottles upside down until ready to bottle.
You can use the open door of the dishwasher to stand bottles on while filling them. You don't need to clean up any spills that way - it'll be cleaned up by the next dishwasher cycle.
Use a bottling wand. They're only about $3 and make the process much faster.
Have a friend cap them as you fill them, if you really want to make things go quickly.
Stuff like this also makes things easier:
http://www.homebrewtalk.com/f35/double-barrel-bottling-now-twice-fast-257264/
BTW, I keg, but still bottle "big" beers that need to age, like barleywines. I use brown Grolsch swing-top bottles.