Best way to sell old stamp & coin collections?

My father recently ped and I am now in possession of his rather substantial philatelic and numismatic collection. I am going to get these appraised soon, and perhaps that company can provide me with the answers I seek, but before I begin that process, what am I really getting into? I don't have the time or knowledge to parse out the items, so I would be looking to unload them all to one or two collectors.