Your research is on the right path...
All the modules in your pictures will work but just focus on correct connections.
ESP01 (third pic) will directly fit on the USB with yellow color header (first picture).
Yes, I know but my adapter is not yet reached so I thought I find another way to program the ESP with just jump cables.
It is possible but it may need more time to research so I decided just wait for the adapter to arrive and save my time doing more research unless I have free time to do more testings.
My friend just passed me an LED fan with a programmer adapter. Maybe it can be used to program the ESP but still I need to find out the Pins connections.
I often use this method, I don't have a serial FTD module
I used Arduino uno, B4R IDE (Board Type - NodeMCU 1.0 ......)
I programmed ESP01/ESP-03/ESP12E with no problems.
Arduino has a serial converter on board, (ATmega 16u2)
It's not a very simple method