What threading module should I use to prevent disk IO from blocking network IO?
Since you're I/O bound, then use the threading module.
You should almost never need to use thread, it's a low-level interface; the threading module is a high-level interface wrapper for thread.
The multiprocessing module is different from the threading module, multiprocessing uses multiple subprocesses to execute a task; multiprocessing just happens to use the same interface as threading to reduce learning curve. multiprocessing is typically used when you have CPU bound calculation, and need to avoid the GIL (Global Interpreter Lock) in a multicore CPU.
A somewhat more esoteric alternative to multi-threading is asynchronous I/O using asyncore module. Another options includes Stackless Python and Twisted.