@Gwion
TBH, I think you might be disappointed with the Pegasos. You are obviously in to the "classic" Amiga hardware and the whole Amiga experience. A Pegasos is not really an Amiga, and it *doesn't* run Amiga OS, except through emulation (and you have already said that UAE doesn't feel like using an Amiga - I can relate to that). I think if you get the Pegasos you will be missing that Amiga feeling, even though MorphOS is a great OS and the board is quite powerful. Of course the decision is yours and you should research it before buying, but I really think you would get more enjoyment from the 060 upgrade to your A1200 as it will really open doors for that machine and make your Amiga experience a lot more fun. (020 to 060 on an A1200 is a MASSIVE jump in speed!)
As for what to do with the A600, I think the great thing about the A600 is, as others have said, its tiny size, and you could exploit that. Get the hard disk loaded up with lots of your favourite Amiga games and keep the whole thing with a couple of joysticks and the PSU in a backpack. Take it round to your mates house, rig it up to their telly, and have a blast playing games which are actually fun :-)
If you want to do something a bit more creative, persevere with DPaint. The interface is a bit daunting at first but persevere - it's not actually that hard once you've tried everything out. Also, since you mention that you like the music in Amiga games, you could download a tracker and make some music on your A600.
Hope some of those suggestions inspire you. Have fun with it :-)
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moto