http://web.singnet.com.sg/~code17/usblcd_index.html most likely uses some microcontroller with usb functionality. Cypress has some for example.
But besides the microcontroller chip itself you also need to write the code for the microcontroller to do all that you want. For the Cypress chips you also need to make your own drivers and if you want to make those for windows you need the windows driver development kit. And I think that if you're not familiar with writing drivers for windows you're going to spend some time with that. With linux things could be simpler but you still need to write the device driver unless someone has already written one that is similar enough to do what you need. A good amount of USB knowledge will be needed for making the driver. Check
www.usb.org for more information and the usb specs.
USB chips from FTDI have ready made drivers for them and that's the choice I'd recommend if you want to make things easier for yourself. FTDI chip is also used in the second link you gave.
I guess the chips from ST could also be used but I believe you need to write drivers for them too.
Also if you're not familiar with any microcontroller yet you might want to choose one that has many examples available in web. Hobbyists often use AVR series from Atmel and PIC from Microchip for example.
Unless you want to get into USB more deeply I think the most important thing is that the hardware you choose has ready made drivers for it.