Correct way to wire USB 2.0 Type C connector?
You want a Type C so connect the CC pins as per Type C as they don't exist in USB 2.
The rest must be done according to USB 2.
If you want to read more about it then the read the USB specs, they have everything you need.
You have also shorted D- directly to 5V, that will damage your PC and your device, don't do that. Besides the pull-up resistor would not be connected to 5V to begin with, but to 3.3V.
Depending on which USB chip you are going to use, the pull-up might be internal, so without knowing what is connected to your connctor, there is no way to answer if you should have a pull-up or not.