Bother? Questions are a great deal why there are things like a.org =).
You can use the internet on a miggy yes. Be aware that the browsers are prehistoric and without extra graphics hardware it will be dogslow in 256 colours max. on an A1200 or A4000. A high end 68k (040 or 060) would also be needed to make it remotely comfortable.
If by listening music you mean MP3s, well, that is possible with 68k but anything below a 060 and it hogs up the CPU. There is however extra addon hardware available (MASPlayer) which hooks to the parallel port and takes the decoding load off the CPU. There are ofcourse also a gazillion mod files available which doesnt take alot of CPU oomph to play.
And there are plenty of art packages available indeed.