You could spend a LOT of time trying to parcel the pieces out one by one, I assure you...but that is the best way to get as much as possible. I guess it depends on how much spare time and patience you have! I would suggest you go to a local antiques shop and ask them who the "best" auctioneers are in the area (and make sure it is not in the same family or group of friends...get several opinions before you start calling)...the serving pieces, as a rule, will be the most popular and worth more than basic items...but not incredible numbers. Platters, for example, are generally $25-40 in that pattern and sugar and creamer sets, $35-55. You can go to a site like REPLACEMENTS.COM and pull individual retail numbers on most patterns...but be advised you likely will not get the prices they advertise...maybe 50-60% at best. And sites like that buy at about 10-20% of retail....
eBay is good choice if you go one by one...just set up a "store" on the site and that way you do not have to keep relisting things...I have many clients who go that route and are happy with the service and prices they get...somebody ALWAYS needs a replacement plate or cup or glass! And the market is worldwide, too....so a good bargain for advertising.
Again, depends on your free time....just be sure to note ANY defect in any piece and always, ALWAYS, fully insure the parcel against damage...and ship signature required. eBay can also be a quagmire of con artists and fraudsters, so protect yourself!