Thank you for your suggestions.

The first "advanced Ancestry form" for a specific census year that allows one to enter race/nationality is the 1870 form.

Entering the data into the "advanced Census and Voter List form", which does permit one to enter race, did give colored persons of my surname, but all were 1860 and later. All of the 1850 entries were white. I am aware that only the names "free persons" appear on the census. Perhaps there were no free colored persons with the surname Thurston in Virginia in 1850.

Entering the data into the African Collection form did not give any census records at all. It gave mostly Freedman's Bank records, USCT Military Service Records and 1890 Veterans Schedules.