I have a 400 and a 600+, and the 600+ is a very nice system since it's more compact than the 400/800 and it has a a real keyboard. Nice find on the 1040ST though I've wanted get one of those along with a C-64 some day.
It's a TAC-2 digital joystick. Probably the most famous joystick there is. Quite good and sturdy, but the fire button gets worn out, so be prepared to fix that if you get one untested. And I do mean _button_, singular. Both of the buttons control the same circuit, so which one is worn out depends on if the player was left-, or right-handed. Compatible with all Atari ST|STe models and all Amigas. Probably compatible with the Atari Falcon too. I prefer the Wico Bat-handle*, but the TAC-2 will do nicely. * http://www.syntaxerror.nu/joy002.jpg
If you want something immediate, remember that earlier Sega pads (three buttons or less) should work. I say "should" because I tried about ten of mine and the only one that worked was a third-party pad for the SMS. Biggest problem for the ST as a gaming platform, as far as I'm concerned. Only providing one button was ludicrously shortsighted.
Know anyone in their 30's? They have one in their storage. If not, ebay: http://cgi.ebay.com/TAC2-Amiga-joys...pt=UK_VintageComputing_RL&hash=item2a0845ee39