You are quite correct to move away from the outdated view of "race" since Humans are genetically too similar, no matter the ethnicity, to be classifiable as different "races".
But we can trace the migrations of the
one race of Humans which left Africa about 150,000 years ago and migrated East and West into two main, initial, branches.
From the main European (West) branch, a series of minor branches and migrations patterns over the last 20,000, years have left about seven groups which roughly fall into the main ethnicity groups.
Interestingly most recently, finer migrationary markers reveal a correlation to country boundaries, roughly as we have assigned them according to the different ethnicities (cultural/linguistic habits).
Genetic study of the relatedness of DNA for Europeans.
http://www.nytimes.com/2008/08/13/science/13visual.html