500pts for Seasoned Pros Best Practice for Connecting to a SQL server for ASP Web and VB

What is the best practice for connecting to a SQL server.

I understand that there is ODBC, OLEDB, etc and I would just be interested in the best practice and also for the ODBC. The method I typically use Option A but have been suggested to use B.
Security is a must and is there no way not to have the UID and Password show?

Option A
***************************************
Const adOpenStatic = 3
Const adLockOptimistic = 3
Const adUseClient = 3
Set objConnection = CreateObject("ADODB.Connection")
Set objRecordset = CreateObject("ADODB.Recordset")

objConnection.Open "DSN=DB_DatabaseName;UID=DBUser;PWD=Password;DATABASE=DB_DatabaseName"

objRecordset.CursorLocation = adUseClient
objRecordset.Open "SELECT * FROM tblTableName WHERE tblTableName.LastName Like '" & LastName & "'", objConnection, adOpenStatic, adLockOptimistic
*****************************************


Option B
****************************************
set db = Server.CreateObject("ADODB.Connection")
  db.open "DSN=DB_DatabaseName;UID=DBUser;PWD=Password;DATABASE=DB_DatabaseName"

function openrs(strsql)
  set rs=Server.createobject("ADODB.Recordset")
  rs.open strsql, db, 3, 1
  set openrs=rs
end function

function closers()
  rs.close
  set rs=nothing
end function

set rs=openrs("SELECT * FROM tblTableName WHERE tblTableName.LastName Like '" & LastName & "'")