I'm putting together a very similar system to the OP
in a Silverstone Precision PS09B. It's a
tiny MicroATX case that can still accomodate 14" graphics card and 4 3.5" HDDs + 1 2.5" (floor mounted). But it's a tricky case to build in that's best for experienced and patient builders.
PROS: Very small (1516 cu. in), large GPU capability (14.1"), sound padding, 120mm intake fan (included) and 80mm front intake mount (empty), inexpensive
CONS: Cramped, 140mm CPU cooler height limit, 92mm exhaust fan mount (empty)
Some mATX case alternatives are:
Thermaltake Urban S1, $45 (2051 cu. in)
PROS: 5x3.5" HDD, 10.1" GPU, lots of vents
CONS: 80mm exhaust, intake fan not included (120mm mount)
Antec VSK-3000, $35 (1517 cu. in)
PROS: Inexpensive
CONS: No USB 3.0 front ports, 92mm intake (empty) and exhaust, no CPU backplate hole
Silverstone Precision PS07, $89 (1516 cu. in)
PROS: 2x120mm front intake fans, 120mm exhaust (empty), 6(!)x3.5" HDD bays, up to 165mm CPU cooler, up to 13.5" GPU, removable HDD cage
CONS: None that I can think of
Silverstone Temjin TJ-08E, $109, (1845 cu. in)
PROS: 180mm intake fan, 5x3.5"HDD+1x2.5" HDD, removable HDD cage, external PSU air feed, large CPU cooler and GPU capacity (can't find specs, but should be similar to PS07)
CONS: Price
Lian-Li PC-A04B, $79, (2037 cu. in)
PROS: 2x120mm intake fans, 1x120mm exhaust fan, 1x80mm exhaust (empty), 7(!)x3.5 in HDDs, Max GPU length 14.5" (requires removing one HDD cage)
CONS: Only 1 USB 3.0 front port
Corsair 350D, $79, (2484 cu. in)
PROS: 140mm intake, 120mm exhaust, lots of space to build in, up to 14.6" GPU, top mount for 240 mm radiator
CONS: very large for mATX case, only 2x3.5" HDD bays
There are several options I haven't gotten around to covering (Define Mini, Nanoxia Deep Silence 4 Mini), but this should give you a good idea of what to expect from a mATX case. Personally, I think either the Lian Li PC A04B or Silverstone PS07 strike the best balance between size, features and cost. The 350D gets recommended a
lot, but it's stupid big for a mATX case (IMO) and is really best suited for users who intend to mount a 240 mm radiator.