Im not a spektrum guy but here is what I could find. That reciever might be using a protocol designed for spektrum satelite but people in this forum post couldn't verify that for sure.
This video breaks down the different protocols between flight controllers and recievers.
It looks like there is just a compatibility issue between the F4 FCs and spectrum receivers. https://github.com/betaflight/betaflight/issues/3677
Since I'm not used to spektrum I can't be much help.
Here is the cheapest alternative I can recommend
About $70 on amazon.
You might be cutting it close. Here's a 6 channel tx and rx for 52$: flysky i6 Then a motor and ESC will probably run you another 30-40$. But youll also need servos (~10$) , battery connectors, batteries, charger, etc. If you already have any of those you very well might be ok.
So far this is what im thinking of getting Quad kit http://www.miniquadbros.com/collections/mini-quad-kits/products/nighthawk-170-kit-for-fpv-racing
Battery charger https://www.amazon.com/gp/product/B01E8MOG1O/ref=crt_ewc_title_huc_2?ie=UTF8&psc=1&smid=A2YGVOB7APVMLY
Is that all i would need?