I'd consider buying a Minimig too, but as far as I know you cannot yet attach any type of hard-drive (or other mass storage device to it). There's only the SD card which can act like a floppy (or hold many floppy images).
The SD card can also hold a hard disk image file.
As it is, (as far as I understand), the Minimig just does a pretty good job of emulating an ECS Amiga 500, but not much beyond that.
I've seen demos of an AGA Minimig - essentially a MiniMig A1200, but I don't think that's been released or perfected.
Too bad, because I certainly WOULD buy a Minimig if it had AGA, real or virtual hard drive support, RTG graphics support, more RAM and a 68030 or 040 emulated CPU. Essentially a "big box" Amiga Minimig (A3000/A4000).
I was very impressed by the Minimig when it first came out (what, like five years ago now), and understood that a basic A500 Minimig was a great achievment, but I thought we'd be at the A4000 level with it now.
The limitations of the Minimig are due to the board design and limited size of the FPGA. The FPGAArcade Replay board will have all of the features you want and more.