How do I create a final map that displays the data in a UTM projected coordinate system in a QGIS project with 4 data layers all having a geographic coordinate system?
As QGIS is a GIS it knows how to handle data of different coordinate reference systems. It can overlay them or transform them as needed. All as long as their metadata is actually correct of course.
To turn your map visualisation into a different projection you can choose a different CRS in the bottom right corner (it should say "EPSG:4326" for you there, click on that). That will turn the map canvas to that projection.
For more complex map productions you should use map layouts, those also support the free selection of the visualisation CRS.