The big-box Amigas were out of reach to most people, but the A500/600/1200 hit a low enough price point to become very popular home computers, at least in Europe, with incredible capabilities compared to the 8-bit generation that people were upgrading from.
Two of my best friends were from 'less than well off' families, and they both had Amigas. My fault - I was lucky to come from a comfortably-off family and had one, which they used to come and use on sleep-overs, planting the seed in their minds.
Ok, the Atari ST may have been cheaper than the Amiga 500, but to make music with it, you had to connect a MIDI keyboard/synthesizer/etc., whereas with the Amiga you could get by just with its built-in capabilities. This is true for the original STs, apparently the "STE" models released in 1989 also had the ability to play sampled audio, but I don't know if that was ever used as intensively as on the Amiga...