Sub selectiveCopy()
Dim bottom As Range, headerRow As Range, cell As Range
Dim targetCell As Range, targetSheet As Worksheet
Dim lastcell As Integer

    'Here is where I want to select the file and store it as "sFileName". This works fine, but doesn't open the actual file, just gets the path.

   sFileName = Application.GetOpenFilename 

   'In order to open the file, I have to run this:

    Application.FileDialog(msoFileDialogOpen)
       .Show
       .Execute

   ' Any way I can just use one? 

Set headerRow = ActiveSheet.Range("1:1")

'Here is where I want to start calling the file variable "sFileName" I get an "object required" error. 
    Set targetSheet = sFileName
    sFileName.Activate

  targetSheet.Cells(1, 1).Select
   lastcell = targetSheet.Range("A1").End(xlDown).Row
Set targetCell = targetSheet.Cells(1, 1)
For Each cell In headerRow
Select Case cell.Value
Case "value1 to copy", "value2 to copy", "value3 to copy"
Set bottom = Cells(Cells.SpecialCells(xlCellTypeLastCell).Row, _
cell.Column)
If bottom.Value < "" Then
Range(cell.Address & ":" & bottom.Address).Copy
Else
Range(cell.Address & ":" & Cells(bottom.End(xlUp).Row, _
cell.Column).Address).Copy
End If
targetSheet.Paste Destination:=targetCell
Set targetCell = targetCell.Offset(0, 1)
targetSheet.Paste Destination:=targetCell
End Select
Next
End Sub