For old games and demos, the A600 is great. You *can* surf the web on it, but that would require lots of time and effort to set up, not to mention $$$ for a CPU/RAM expansion. Same goes for 3.9. (I'd stick with a maximum of 3.1 on a stock A600.)
The A1200 does everything the A600 will do, plus it has AGA... and CPU expansions are easier to find and less expensive.