For data transmission / reception, one of the less expensive options today is a pre-built module around the nRF24L01+ Transceiver IC. These modules typically offer a built-in PCB-trace antenna, 250 Kbps to 2 MBPS bandwidth before error correction, and are tried and tested.
Most important, they save you time in debugging and antenna tuning. After thousands of people have used these modules, which are built on the manufacturer's reference designs after all, most of the kinks are pretty thoroughly ironed out. Also, being able to tap the experience of many others on the internet who have used such a module, counts for a lot when trying to resolve issues.
For instance, this listing on eBay is for a mere US$2.10 with free international shipping. It uses the 2.4 GHz band, which does not need licensing for low power use in most countries.
Another alternative is this 433 MHz band transmit / receive pair of modules (just 9.6 Kbps though), in case you specifically want to stay with transmit-only and receive-only designs. US$1.99 for the pair makes it pretty attractive.
Of course, in each case, you could as well build your own module starting from the IC manufacturer's reference design, and thus learn while implementing your radio functionality.
It is unlikely that the price advantage of massive volume production can be beaten, though.
Best Answer
AM signal has a good reference - the carrier. AM receivers are generally designed to have an automatic gain controlling circuit (=AGC) which tries to keep the DC voltage that's obtained by rectifying the carrier in the diode detector constant. It's quite possible that a distant station needs 1000x higher total power gain than another which is either strong or placed in the same city as the receiver.
The simplest crystal receivers do not have that gain control and with them the volume varies as you thought.
There's a variation of AM signal - the SSB - which doesn't have a carrier. If someone isn't talking right now, SSB signal is non-existent. Gain control must either be manual or cleverly increase the gain slowly if nothing is detected until either the noise jumps too high or some strong signal appears.
FM radio signal has a carrier. AGC is used to adjust the signal level to be suitable for the FM demodulator circuit.