I'd like to know if this Nucleo 144 board is supported by Keil, since the box says so. In the new project wizard however, this board does not appear to be supported. Can I choose any of the supported boards?
The STM32F767 is a Cortex-M7.
Yes, Keil tools can generate code for Cortex M7:
www2.keil.com/.../selector
At that level, it makes no difference what board the chip is on.
ST provide board-specific code for their boards. Have you studied the documentation and other support materials on the ST product page ?