Yes, you can go to the courthouse for property records. Keep in mind that a few of the older buildings may not be standing.
Try Find-A-Grave for the cemetery records.
The Gilliam County Historical Society has a wealth of information about the people who lived in the community. I don't know what you are looking for in terms of "good searchable records." There are photgraphs, books, card files with newspaper items, school year books...too many to name.It is closed from October-May, so you'd better hurry if you want to make it this season.
The Times-Journal has been a weekly newspaper published since 1886 under variations of the name, including the Fossil Journal.
Am I correct in assuming you are looking for the family of Hannah McFarlane Anderson?