Load your Excel sheet into ArcMap as a table using Add Data... (Drag and drop generally will not work with excel sheets).
Right click the table and choose Display XY Data.
Use Long for the X field, Lat for the Y field.
Select Edit... under the Coordinate System of Input Coordinates and select WGS1984 for your coordinate system. Run that to get an XY Event layer that you can buffer.
Open the Buffer tool under the Analysis-Proximity tool box.
For Input Features, use your XY Event layer. Output is whatever location you want to use for your output.
For Distance, select the radio button next to Field and then select the Radius Field.
This last step is important, and requires you to know what coordinate system you want to use for your output. Your coordinate system needs to be in meters. (If you cannot use a coordinate system in meters, mention it here and we can talk about Project your results or adding the unit of measure to your radius field.) For the last step, click Environments... at the bottom of the tool. Expand the options for Output Coordinates. Select As Specified Below, and click the hand holding a paper icon next to the box below that dropbox. Select the coordinate system in meters that you have chosen. Click OK to close that dialog. Click OK again to close the Environments settings. And then click OK a third time to run the tool.