But I need something for that [transmitter] to plug into. Could I use this, and plug this into the USB port of my HAOS machine?
You linked a ESP01 programmer, rather than an ESP01 board. You want to connect the transmitter into the ESP01 board itself. You can then program the ESP01 with the ESP01 programmer you linked. See the writeup here for ESP01 programming.
You could instead use a slightly more expensive ESP32 that you can plug directly into your computer to program or into a power brick once it’s all working. This is significantly easier to deal with.
(Note my links aren’t recommendations, just the first refs I saw on Amazon. Lots of options.)