Choose CountyDemoModified.shp and bring into a new QGIS project.
Toggle editing ON
Open Attribute Table.
Sort the FIPStxt column by clicking on the column name. Click the row number where the FIPStxt is 31001 (1621), hold shift, scroll down and click on row number 1713, and release shift. Nebraska's state number is 31, and you just selected all of the NE counties.
Close attribute table.
Right click on Layer and go down to Export. Click Save Selected Features as...
Save as: ESRI shapefile. Click three dots next to File Name to choose where to save the shapefile (in its own folder on your desktop, i.e. a new folder called SubsetQGIS) and name Nebraska.shp. Click ok.
Remove the counties layer for the whole U.S. Keep your nebraska layer.
Right-click on the nebraska layer > properties > symbology: change single symbol to graduated, click the equation symbol next to the column selector and input the same equation as the circle and heat maps, change the color ramp, choose classification "mode," and set classes to 5.
Project the map to Albers Equal Area Conic: Project > Properties > CRS tab
Zoom into NE and export as PDF: Project > New Print Layout > [name the map layout] > add map > export as PDF.
Select the map, go to Object > Clipping Mask and select Release. Remove neatlines.
Rotate nebraska so it looks straighter. Add title and legend. Add design elements. Export as PNG and save as PDF.