Most of the games you'll want to play are probably 8-bit and will run fine on any of those three models, whereas the 16-bit games will require an Apple IIGS. I personally prefer the IIGS due to its backward compatibility, greater on-board RAM, and faster CPU -- it can do everything the IIe can do, and then some. But the IIe and IIc certainly have a more retro feel to them.
As for choosing between the 8-bit models, it depends on whether you intend to make additional investments in the hardware. The IIe is more expandable, while the IIc is more compact and portable.
For getting files off your Mac, I'd recommend ADTPro. There are literally dozens of other methods for transferring files to the Apple II, but not all of them are as obvious or painless as this one — though the additional cables you'll need may cost you more than the Apple II did!