Intel Core i3 4340 3,6GHz, TDP 54W
If you don't need the IGP, it would seem a waste of money: a Pentium G3420 would serve you well, although it's a little slower. Otherwise, a Core i5 4430 or 4670 (not K, maybe S cause they could be found for some money less than regular SKUs these days) may offer a better value.
Corsair Vengeance Low Profile DDR3 PC12800/1600MHz CL9 2x4GB
It's a standard profile, basic and overrated memory: low voltage Kingston or Crucial should be preferable, even some G.Skill Ares might worth.
Asus Gryphon Z87
As said by Abula, a Z87 is a total overkill, unless you buy a K CPU: but then your Mini Ninja wouldn't be adequate.
Providing that the relevant TUF Design isnt' sought after, ASUS H87 Pro (adviced by Abula), ASRock H87M Pro4, and MSI H87M-G43 are all viable choices.
But I am worried that the graphics card is too weak (not matching the CPU), but given the low height of the Antec Fusion it is the best passive card I have found. Or, can you recommend any other that fits in the Fusion case? Are there any silent (enough) graphics cards with active cooling?
If you're a gamer, the fastest fanless card available is the Power Color HD7850 SCS3 (AX7850 1GBD5-S3DH), but it is 132mm tall (from the PCI-E slot) and I don't know if the Antec can fit, moreover it's pretty rare and expensive.
There are several quiet cards today: I would give a look at ASUS DC-II, XFX DD and (maybe) Radeon MSI (IME Nvidia MSI seems to have all crippled BIOSes).
Can the cooler handle the Intel 4340 CPU? Could it even handle an Intel 4670K (TDP 84W)?
Haswell chips may run pretty hot compared to previous generation Core i3/i5s: you have to fine tune your fan behaviour; anyway, I don't think it can handle an oc'ed i5, and if you don't overclock a K SKU, as said a regular quad is then advisable.