Is there a good description of what those $100 in parts for satellite work are? Or better yet, something purchasable that's likely to work? I've been wanting to get into it, but I've never found a really accessible guide to getting started in satellite communication.
Then you can get the transmitter and receiver together, in a package like the regrettable BaoFeng UV-5R: https://www.amazon.com/BaoFeng-UV-5R-Dual-Radio-Black/dp/B00... . This is a terrible radio. Their quality control is so bad that you sometimes commit a federal offense by pressing the transmit button—and for $100, you can't afford the test equipment to tell! So maybe use it as the receiver in a two-radio setup, and transmit with something like a Wouxun KG-UV9D.
A Kenwood TH-D72A is an excellent choice to do the transmitter and receiver jobs, but hundreds of dollars. A Yaesu FT-60 is a great choice too, but it won't have full duplex—so you can't be sure your signal is getting out without help.
For all of these, you'll end up wanting miscellaneous coaxial cable and a bunch of ends. Hams tend to build up a library of crimpers and spare ends and such, so look to borrow from a friend or a club as you get started. The 75 Ω cable that's ubiquitous for television signals will totally work, but you'll have much less loss and much much less stress on components if you buy 50 Ω cable.
Why not try the tutorial at https://www.rtl-sdr.com/rtl-sdr-tutorial-receiving-noaa-weat... ? If that works, you can expand from there: the tutorial teaches you a huge amount about aiming at satellites and the physical work necessary to capture signals from space.
I haven't looked into satellite work in fifteen years or so, but back then it was definitely possible to work the LEO FM repeater satellites using a handheld and a small yagi - typically two elements 144MHz, five on 432MHz if memory serves.
With handhelds being dirt cheap and a yagi cut from a measuring tape being an option, I don't think getting on satellite for $100 sounds undoable.
You could make a good tape measure yagi and use it with a cheap radio like the UV-5R. It needs to be dual-band (440mhz and 2m); AMSATs are usually duplex.
