Well well well, Mr Electronic Steve!!
Just that man I have been looking for (I hope :-D)
See.I was just talking about the Amiga CD32 game console
in another topic:
http://www.amiga.org/forums/showthread.php?t=18440 Check it out and tell me if your willing to take on such a project as your first Amiga experiment :-D
Yes.... Amiga released a Games console based on the Amiga 1200 and A4000.......
By the way.....I dont think you need to purchase Golden Axe! I believe its probably free for download at backToTheRoots.org where you can get tons of free commercial games for the Amiga. Also Outrun, SPace Harrier, Shinobi and other Sega games (I think)