Once the coordinates are entered, navigate to the Table of Contents and right-click the table > Display XY Data.
Select the X Field as Longitude and the Y Field as Latitude from the dropdown menu.
Click the Edit button to select the appropriate geographic coordinate system (WGS 1984 is used for most GPS points), and click OK. This adds a layer to the map named '<geodatabase filename> Events'.
Change the coordinate system of the data frame to the desired State Plane system.
Right-click the added layer and navigate to Data > Export Data.
Select the 'Use the same coordinate system as: the data frame' option, and select the output location. Click OK. The new feature class is added to the map.
Open the attribute table of this new feature class and add a new text field.
Right-click the new field and navigate to Calculate Geometry. If prompted about being outside of an edit session, feel free to proceed or begin an edit session. In the Calculate Geometry window, select the 'X Coordinate of Point' property, and 'Use the coordinate system of the data source' option. Click OK.
The State Plane X-coordinates are now in that field.