ANY Power PC running ANY version of the classic Mac OS can run ANY program designed for ANY classic mac. How's *that* for backwards compatability? The only trick is being able to get the software onto the mac. I have an inherited tangerine iMac I use for running older mac stuff. I can transfer to it via CD/DVD or USB stick, or direct from the network/internet via ethernet or Airport wireless. For floppies...well, unless I find a USB floppy drive, I'm stuck finding disk images.
For both OS 7ish era useage and Apple II backwards compatibility, any of the 24-bit "dirty" LC series (including Performas, Quadras and regular old LCs) can use the Apple II card that was designed just for these machines. It's basically an Apple IIe on a card. Just make sure you find the Y-cable for disk/joystick usage, otherwise you won't be able to connect a Disk II drive to it.