[mumrah]

Cheapest? A Chinese radio off Amazon, e.g., https://www.amazon.com/BaoFeng-UV-5R-Dual-Radio-Black/dp/B00.... This will allow you to tune in to local repeaters and listen. N.B., you cannot legally transmit without a license which is easy and cheap to obtain http://www.arrl.org/getting-licensed.

After getting licensed, you'll probably get frustrated with the UV-5R and look into a more capable hand held unit, or a mobile radio. These start at around $150 and go up from there (plus antennas, power supplies, etc).

[kqr]

Thanks! I'm well aware I'm not legally allowed to transmit and don't plan to either. I'm just fascinated by the prospect of receiving invisible waves and having them translated into sound in my hand.

Can I read somewhere about which frequencies are used by ham operators, and descriptions of things like UHF and VF and narrowband and such?

[Steltek]

Google "ARRL Band Plan"

http://kk4mes.com/wp-content/uploads/2015/02/arrl-bandplans....

I roughly split spectrum in my head as "longer waves" (kHz, AM radio, needs impractically large antennas), "HF" (thousands of miles of range, largish antennas), "VHF/UHF" (line of sight, 25 miles, walkie talkies), and "microwaves" (1GHz+, short range, tiny antennas for wifi).

Someone already mentioned the Baofeng style of cheap Chinese radio. They're good enough but they also produce pretty dirty signals that there's a chance they aren't legally compliant. That being said, everyone seems fascinated with them right now so they get away with it for the moment. I wouldn't let that stop you since if you stick with it, you'll move up soon enough and it'll become the backup/beater radio.

I'll add on that $25 RTL-SDR (get a "TXCO" one like a Nooelec Blue) is also a pretty cheap entry into listening to absolutely everything. With that, you can start making antennas, listening to satellites, running your own FlightAware ADS-B scanner, etc. To listen to HF, you can add a $75 upconverter.

[vvanders]

If you do pick up a Bao Feng be sure to grab a 16" whip like this: https://www.amazon.com/Authentic-NA-771-15-6-Inch-SMA-Female...

Will do wonders for what you'll be able to hear(and send). I've got a similar Diamond one on my VX-8DR and I can pick up the repeaters ~20mi away. Can't hit them though, but that's what cross-band is for :).

I'm able to run a pretty resonable APRS setup w/ BF-F8HP + above and a mobilinkd for ~$120.

[btreecat]

If you don't have any interest in transmission (for now) you should probably pick up an SDR dongle since they can tune a much wider range of frequencies, and are cheaper.

http://www.rtl-sdr.com/