Nothing like jumping in at the deep end. Running before you can walk comes to mind However it should be possible.
Insert a module into Outlook VBA and copy the following into that module.

Modify the line - Const strPath As String = "C:\ZipTest\"
to reflect where you want to store the unzipped files. This folder will be created if not present.
Modify the line - strDate = Format(Now, " dd-mm-yy")
to reflect the date format you wish to add
The macro creates a dated sub folder e.g C:\ZipTest\Unzip 23-09-14 - with the name at - Const strSubFolder As String = "Unzip"
that contains the files from the zip.
The UnzipAttachments sub is intended as a script to be run from an Outlook rule which identified the messages to be processed. The process is tghus run as the messages arrive in the inbox. I have included TestUnzip to test the macro on a selected function.
Thanks to Ron de Bruin for suggesting the method used for the extraction routine - http://www.rondebruin.nl/win/s7/win002.htm 


Option Explicit

Sub UnzipAttachments(Item As Outlook.MailItem)
Dim olAtt As Attachment
Dim strFilename As String
Const strPath As String = "C:\ZipTest\"        'Folder to save temporary files
    If Item.Attachments.Count > 0 Then
        For Each olAtt In Item.Attachments
            If Right(LCase(olAtt.Filename), 3) = "zip" Then
                If Not FileExists(strPath) Then MkDir strPath
                olAtt.SaveAsFile strPath & olAtt.Filename
                UnZipFile strPath & olAtt.Filename, strPath
                Kill strPath & olAtt.Filename
            End If
        Next olAtt
    End If
lbl_Exit:
    Set olAtt = Nothing
End Sub

Private Sub UnZipFile(Fname As Variant, strPath As String)
Dim FSO As Object
Dim oShell As Object
Dim FileNameFolder As Variant
Dim strDate As String
Const strSubFolder As String = "Unzip"

    'Create the folder name
    strDate = Format(Now, " dd-mm-yy")
    FileNameFolder = strPath & strSubFolder & strDate & "\"

    'Make the normal folder in DefPath
    MkDir FileNameFolder

    'Extract the files into the newly created folder
    Set oShell = CreateObject("Shell.Application")
    oShell.NameSpace(FileNameFolder).CopyHere oShell.NameSpace(Fname).Items
    'MsgBox "You find the unzipped file(s) here: " & FileNameFolder
    On Error Resume Next
    Set FSO = CreateObject("scripting.filesystemobject")
    FSO.DeleteFolder Environ("Temp") & "\Temporary Directory*", True
lbl_Exit:
    Set FSO = Nothing
    Set oShell = Nothing
    Exit Sub
End Sub

Private Function FolderExists(ByVal PathName As String) As Boolean
Dim lngAttr As Long
    On Error GoTo NoFolder
    lngAttr = GetAttr(PathName)
    If (lngAttr And vbDirectory) = vbDirectory Then
        FolderExists = True
    End If
NoFolder:
    Exit Function
End Function

Sub TestUnzip()
Dim olMsg As MailItem
    On Error Resume Next
    Set olMsg = ActiveExplorer.Selection.Item(1)
    UnzipAttachments olMsg
End Sub