Before you can connect device A to device B you ought to learn something about the interface and capabilities of both devices.It seems to me that STM32F407 is suitable for all three examples. But I can't say anything about any particular monitor because I have no idea about it.
So you want to connect an MCU to a display.
Consider the following displays, how each works, and the interface required. Each one is not compatible with the other.
2) Seven-segment display
3) LCD custom display
4) LCD alphanumeric character display
5) LCD Graphics display
6) VGA monitor
7) DVI monitor
8) HDMI monitor
Which ever you choose, you need to read up about the electrical interface and the protocol used to drive the display. On top of the hardware, software is required to drive the display. Don't assume that the software is already there to drive the display.