Well , looks like this forum is certainly alive and very active - so many responses so fast.
Looks like from what I read that the Minimig is probably the best solution for me - as in new hardware to run the old games for when my existing Amigas die from old age or whatever.
Thanks for all your inputs and ideas.
The Minimig v1.1 is a great little board and much has been done to improve it since it was first invented, but I would point you toward MikeJ's Replay board as an even more improved, similar concept, that has more options, and will eventually run more cores from different computer and arcade systems. Plus, if the 060 daughter card goes into production, it will be equivalent to, or surpass the fastest 68060 Classic Amigas and include most of the best additions to Classic Amiga systems, such as USB, Ethernet, more RAM and a Scandoubler, all in a smaller and more modern package. The Replay is like a Minimig on steroids.
Another interesting project that you might be interested in is the Natami, but I don't have any idea when it will be ready for public consumption.