I follow the lead from professional winemakers -- they get a bag of corks (typically 1,000+), cut the bag, and dump it into the bottling line's hopper. Same with bottles, they come out of the case and into the bottling line.
While I don't go through as many corks at a time, I cut a corner of the original bag, wipe the counter with K-meta solution to ensure it's clean and sanitized, and line up corks on the counter. When done, I press the air out of the bag, roll the empty part tight to close it, and secure with an office binder clip.
Similarly with bottles -- I clean them well and let dry completely, and visually inspect -- any that fail get re-cleaned (this is rare). They go mouth down in clean cases until use. They are dry so there's nothing to grow on, and being mouth down they are sealed so nothing (e.g., bugs) can get in. At bottling time I again visually inspect all bottles as I line 'em up, setting aside any that have anything odd. Fill-n-cork.
