Sounds like an excellent application for Twisted. Here are some web-related examples, including how to download a web page. Here is a related question on database connections with Twisted.
Note that Twisted does not rely on threads for doing multiple things at once. Rather, it takes a cooperative multitasking approach---your main script starts the reactor and the reactor calls functions that you set up. Your functions must return control to the reactor before the reactor can continue working.
