Jayson:
You can use either LabVIEW or CVI as the programming environment to communicate with your scope. Both are sufficiently general purpose development environments to work with any instrument. For that matter, you can use gcc if you really want to.
The real question is what protocol/API to use, and the answer is, as you suspected, to use VISA. The main networking based protocol that most Tek scopes support is the LAN Instrument Protocol (aka VXI-11, but that's not really important), and NI-VISA 2.6.1 or higher supports that protocol well. NI-VISA 3.0 is available on all the OSs we currently support.
Dan Mondrik
Senior Software Engineer, NI-VISA
National Instruments