If you want to handle a signal in the analog domain, it doesn't take much in terms of electronics. AM radio can be received using a crystal radio, 100+ year old technology, if the signal is strong enough. You need 6 parts, antenna, ground lead, coil, capacitor, diode, headphones.
To receive FM mono, you could use a diode radio, tuning off to the side of the carrier.
To receive FM stereo, you need a fair bit of electronics, including a phase locked loop.
Receiving FM stereo with RDS, etc. is a quite challenging thing to do in terms of signal processing. It is the only time my laptop really just can't keep up in terms of all the experimenting with Gnu Radio. It has the combination of high complexity, and high bandwidth that multiply out to a large compute load.
That is why the warning was included.
--- And now, for more info than you asked ---
I've had an SDR dongle for years, and got back into it when the plague hit. I've received AM, FM, Single Sideband, all are fairly narrow bandwidth, so I have plenty of compute power to spare for making complex graphs.
One of the "radios" I've built can receive all 5 NOAA weather radio channels at the same time.
Another receives the local VOR (VHF Omni Range) station, and plots the direction to the transmitter.
I can record an arbitrary 2 Mhz wide swath of bandwidth to disk (SSD, actually) in real time until I run out of disk space, and then post-process it later in any manner of my choosing.
GNU radio is free software, and so much fun to play with.
If you're a reddit user, I recommend checking out
https://www.reddit.com/r/GNURadio/ https://www.reddit.com/r/RTLSDR/
You can listen to SDR on the net at http://www.websdr.org/