These are the steps I take. Others may have better suggestions:
First, I look at each public tree. I click on each of the common names. If the person or people are from the same general area and the same time frame, I look closer. (For example, a lot of my ancestors immigrated to New England in the 1600s to 1700s. I don't pay attention to the same surnames who are from Virginia. Those are probably not my family.) If they are from the same town or village, but I don't see exact matches, I look at both our charts to see if they go back to a common ancestor a few generations back. I also look at our chart's list of siblings on the chance one of us just didn't find the parents.
Then I glance through all the surnames in case there is a slightly different spelling to look at. I certainly don't remember every name on my chart, but I do remember most back 5 or 6 generations.
If I see the surname of one of my many "brick wall" grandparents, I copy all the names on their chart (mostly still in the same region) and paste it into a text file. I watch that list and when I start seeing a patters - the same surname family repeating over and over - I focus on that family to find their lost son or daughter. That's where a paper trail comes in. DNA shows me a MRCA (most recent common ancestor) but it is up to me to connect that person to my ancestor through the descendents.
I don't pay attention to the Ethnicity Report because it represents ancient migration and is not often relevant to recent genealogy.