Sorry - I overlooked the fact that you are working on a network.  
Unfortunately, the exact printer name that VBA wants can be different from
one machine to the next (the port names are sometimes different it seems).  
You will probably need to capture the available printers and try to
reconstruct the printer name (Printer On Port).  

In the code below, oPrinters returns a collection of installed printers and
their respective ports.  My approach is to loop through the collection of
intalled printers and match them to your preference list (arrPrinterList).  
Then set the activeprinter to the one that had the lowest match in your list.

Option Explicit

Sub Test()
Dim WshNetwork As Object
Dim oDrives As Object
Dim oPrinters As Object
Dim strDefaultPrinter As String
Dim arrPrinterList(1 To 4) As String
Dim varResult As Variant
Dim i As Long
Dim lngTemp1 As Long
Dim lngTemp2 As Long
 
arrPrinterList(1) = "Office Printer"
arrPrinterList(2) = "Epson Color"
arrPrinterList(3) = "EPSON TM-H5000II Receipt"
arrPrinterList(4) = "HP 1200"

strDefaultPrinter = ActivePrinter
 
Set WshNetwork = CreateObject("WScript.Network")
Set oDrives = WshNetwork.EnumNetworkDrives
Set oPrinters = WshNetwork.EnumPrinterConnections
For i = 1 To oPrinters.Count Step 2
 varResult = Application.Match(oPrinters.Item(i), _
  arrPrinterList, 0)
 If IsNumeric(varResult) Then
  If lngTemp1 = 0 Then
   lngTemp1 = varResult
   lngTemp2 = i
  ElseIf varResult < lngTemp1 Then
   lngTemp1 = varResult
   lngTemp2 = i
  End If
 End If
Next i

If lngTemp1 > 0 Then
 ActivePrinter = oPrinters.Item(lngTemp2) & " On " & _
  oPrinters.Item(lngTemp2 - 1)
Else
 Application.Dialogs(xlDialogPrinterSetup).Show
End If

'Print Your Documents
ActivePrinter = strDefaultPrinter

End Sub

Here is some code posted by others on this newsgroup (and reposted by Tom
Ogilvy) to capture the installed printers.  KeepItcool used API calls in his
example (and he may have updated his macro - you could google his name and
check).  I used Jim Rech's code in the above macro.  

Posting by KeepItcool

Option Explicit

Private Declare Function GetProfileString Lib "kernel32" _
       Alias "GetProfileStringA" _
       (ByVal lpAppName As String, ByVal lpKeyName As String, _
       ByVal lpDefault As String, ByVal lpReturnedString As String, _
       ByVal nSize As Long) As Long

Sub showlist()
 MsgBox Join(PrinterList, vbNewLine)
End Sub

Function PrinterList()
 Dim lRet        As Long
 Dim sBuffer     As String
 Dim lSize       As Long
 Dim avTmp       As Variant
 Dim aPrn()      As String
 Dim n%, sPrn$, sConn$, sPort$

 'Get localized Connection string
 avTmp = Split(Excel.ActivePrinter)
 sConn = " " & avTmp(UBound(avTmp) - 1) & " "
 'Get Printers
 lSize = 1024
 sBuffer = Space(lSize)
 lRet = GetProfileString("devices", vbNullString, vbNullString, _
   sBuffer, lSize)
 sBuffer = Left(sBuffer, lRet)
 avTmp = Split(sBuffer, Chr(0))

 ReDim Preserve avTmp(UBound(avTmp) - 1)
 For n = 0 To UBound(avTmp)
   lSize = 128
   sBuffer = Space(lSize)
   lRet = GetProfileString("devices", avTmp(n), vbNullString, _
     sBuffer, lSize)
   sPort = Mid(sBuffer, InStr(sBuffer, ",") + 1, _
     lRet - InStr(sBuffer, ","))
   avTmp(n) = avTmp(n) & sConn & sPort
 Next
 PrinterList = avTmp
End Function

================================

This posting by Jim Rech may be useful as well - certainly simpler:

From: "Jim Rech" <jarech@kpmg.com>
Subject: Re: Setting active printers will Excel 97 VBA
Date: Thu, 19 Oct 2000 14:04:56 -0400
Lines: 9
Newsgroups: microsoft.public.excel.programming

This macro enumerates printers and their connections.  Parsing it you may be
able to construct the syntax ActivePrinter wants:

Sub a()
  Set WshNetwork = CreateObject("WScript.Network")
  Set oDrives = WshNetwork.EnumNetworkDrives
  Set oPrinters = WshNetwork.EnumPrinterConnections
  For i = 0 To oPrinters.Count - 1 Step 2
     Debug.Print "Port " & oPrinters.Item(i) & " = " & _
      oPrinters.Item(i + 1)
  Next
End Sub

--
Jim Rech
Excel MVP
--------------------------