I started to make chiptunes for ZX Spectrum computer in 1989.
ZX Spectrum 48K has 1-bit sound by default, but one can also connect an AY-interface to the computer (existing since its very beginning in 1982 and even earlier because first AY-interfaces have been built for ZX81 computer - 1981).
Anyway - then Spectrum has the same standard possibilities what Amstrad CPC, Atari ST or MSX have (they using the same chip standard: AY/YM). It means 4-bit sound, 3 channels + white noise generator, square wave and several buzzers. Or - instead of it - I can use 3 channels of 4-bit digital sound but then I have to fit all samples in 48Kb of RAM. 
In case of chip-music, as "standard possibilities" I understand AY/YM working in 50hz (Atari ST can use this chip with 200hz of speed which gives them better audio effects. Cry cry!!).
So that's my weapon of choice: ZX Spectrum 48K with AY-interface. (Well, actually last times I found it's YM but the difference is minimal).
For making chiptunes I use ZX Spectrum's Sound-Tracker 1.1
...and for digital MOD-like music I use Sampletracker 2.0 and 2.1
In 2002 I founded AY-RIDERS band. We play chiptunes on our Spectrums (48K, 128K and higher models).
AY-RIDERS' music You can find here: http://ay-riders.speccy.cz/
In 2010 I founded YM-DIGITAL band. We play lo-fi digital music (MOD 4ch and MOD 6ch) on our ATARI 520ST machines, with usage of ym2149 chip only. Our music is here: http://ym-digital.i-demo.pl/
My solo music You can find here: http://yerzmyey.i-demo.pl/
Except the above, I also often use:
SoundTracker on ZX81;
E-Tracker on SAM Coupe computer (Spectrum Advanced Machine);
MusicMon on ATARI 520ST;
DigiComposer on ATARI 520ST;
ProTracker on ATARI 520 ST;
Hex-Tracker on ATARI 520ST;
Octalyser on ATARI 1040 STE;
OctaMED on AMIGA 500;
DigiBooster on AMIGA 1200;
Digital Home Studio (DHS-Tracker) on ATARI Falcon 030
.............and many others............................
PS: No good deed will escape unpunished.
