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I want to spatially join polygons (geologic features, major aquifers) to where the NHD polylines (rivers/streams) fall. I want to be able to click on a polyline and see what geologic feature or major aquifer the NHD polyline flows through it. Do I use the spatial join for this? I have joined other attributes like Stream Order, Velocity, Watershed area because I can join them based on a ComID because all information came from NHDplus. I am using ArcMap 10.4.

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Probably a spatial join, yes. But think about whether there will be many lines that fall in multiple polygons, and if that matters to your project. The geoprocessing spatial join tool (as opposed to the ArcMap menu join) has more options to, for example, join to the polygon where the line's midpoint falls. If you want the lines to be divided where they change polygons, then look into the Identity tool. Identity requires a higher license level, but I am sure there is a way to use a few steps to get similar results using other Basic license tools.

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