Herfe is what I do. Never had a burst, had only one bottle in over a year pick up contamination.
Put enough caps for the batch in a bowl of no-rinse. Let 'em sit there through the entire bottling process, from boiling priming sugar, siphoning and so on.
Fill all bottles - no loose caps on top, just don't let anything touch the bottle tops. Put the bottles back into the cases or six pack holders so they can be moved easily. I leave them there to fill; once the bottles are all filled, I carefully - without touching anywhere near the opening - put them on the counter.
I use one of those two-arm cappers with a little magnet to hold the caps. I clean my hands thoroughly, dip them in the no-rinse, and start capping, one at a time. I leave a towl on the counter where I am working to wipe off the bottom of the bottles after I cap them, then replace them in the case or six pack holder. This last step is because I use those over and over, and I expect that sooner or later the accumulated drips will cause the box glue to fail with catastrophic results.