I'm not at all new to the topic of building computers, but I don't know much about small form factor hardware, so here is my question/concept:
I have an office, and a home, I like to bring a computer back and forth between the two because A) I don't know how safe the computer would be alone in the shared office-space, and B) I want something powerful since I game a good bit (and I would like a second gaming rig around the house) and C) my job (physics grad student) can involve some CPU-intensive simulations, etc at times.
-fit in a backpack/laptop case
-Be significantly more powerful than your average laptop.
-no monitor necessary, I'll leave a cheap one at the office.
mini-itx vs matx - obviously mini itx is smaller, but more expensive in general. I also have a phenom 965 BE and matx board to go with it - so I could re-purpose those parts, underclock the chip, and buy a new mobo/proc for my main rig. On the other hand, I could just buy new chip/mobo, no difference really, would need one in either case anyway - but I assume I could get more for the same price if I'm buying a new atx board instead of mitx - haven't looked prices on these up much yet.
something that will fit a big shuriken perhaps ~3-4in thick? but with minimal dimensions otherwise (slim). This is my main concern, finding a nice slim case is a pain.
Recommendations on mobo/case/psu all appreciated. If I buy a new proc/mobo I will probably go with an intel (2500k I guess, but maybe something lower-power if necessary) - Obviously the AMD APUs are an option if I can't make a decent gfx card fit in one of these cases, but with a pcie ribbon, and perhaps some other adapters and rigging, I might try to throw a gtx 550 or something in there, depending on what the psu can handle.
I've built a few SFF's over time and nothing that I know of is going to fit into the space you specify, be able to provide the graphic support for gaming, sufficient power, sufficient cooling and storage. You need a good laptop with a dedicated graphic card. Perhaps someone else has some insights.
An A8-3870K might be worth a look if you would be happy with the HD 6550D graphics. It would mean you could go for the smallest case imaginable because you don't need to worry about space for a graphics card.
If one of those cases meets your needs and fits in the backpack then ok. I assumed those were all larger than you wanted. Careful on the Hdd. I would use the WD Black series and even look for info on shock mounted drives because you will be handling it so much. Using onboard video will reduce heat but the graphics may not mee your needs (that was my bigger concern plus the heat and power needs)