As far as I'm aware, you will not be able to use the LCD TV as a remote monitor - but maybe someone knows more about.
I'm not sure what you want to do with the music - listen to tracks on the PC via the stereo ? In that case it would probably be just as easy to put your music onto CD and play it that way, but its your choice.
If you want to do this then all you need is some wireless network device. This could be either a PCI card or a USB device. If you only need to connect the two devices then thats all, you won't need a router. 802.11b/g are two types of wireless protocols basically. The main differences are 'b' works at 11Mbps and 'g' at 54Mbps. If I remember correctly, the 'b' can act over a greater distance, but I can't remember the figures.