I am connected to my router via cable now (USB, is it slower btw?), how can I disable my wireless model on my computer now since I don't need it?
The easiest way to do this depends on what sort of hardware you're using.
Is it a laptop? There may be a function key combination or even a physical switch to turn it off.
Is it a desktop with an internal card? Disabling the adapter in the network controls or in Device Manager may be the easiest thing to do. (EDIT: See Kyle's answer for specifics on this)
Are you using a USB dongle? Just unplug it!
All that said, if you're not actively using it, there's really no harm in leaving it enabled (except possibly if your machine is painfully slow); just disconnect from the network.
Start>control panel>network and sharing center>change adapter settings(on the right side) right click your wireless adapter and click disable. You can also disable it from device manager.
EDIT: I forgot about windows key + X that will bring up the mobility center and you can easily turn off your wireless there.