I want to be able to run the case fans as quietly as possible.
Get an Asus board, the fan control is very good. The Z77 chipset has all options. If you don't overclock (non-K CPU) the H77 chipset has everything but overclocking. Z77 boards are more expensive, but have more ports (USB 3.0, SATA) and some have wireless on board.
Which board to get depends on what other cards you need to plug in: Sound card, TV tuner, etc.
ASUS P8Z77-V is packed with features, but expensive.
Intel i5 3570S or i5 3470
Or is there a better Sandy Bridge CPU which will be good for gaming yet quiet and relatively low power?
Idle power is very low for ALL Ivy Bridge CPUs and load power non-OC, too.
Get the i5 3570K.
If you ever need more power, you can overclock (on a K CPU), if you don't the price premium to 3570 is very small. The 3570k has the HD4000 graphic, which by itself is unremarkable, but Intel Quick Sync speeds up video recoding and uses the integrated graphics. The HD4000 in the 3570K is faster than the HD2500 found on most other chips.
ASUS GeForce GTX 660 Ti Direct CU II 2 GB
Seems like the quietest card around that will be more than adequate for 1080p gaming.
Good card, quiet out of the box.
8GB of whatever is best for the Motherboard?
1600MHz is enough, I recommend Corsair. G.Skill is good, too.
Silverstone Grandia GD08 or Lian Li PC-C60
The Lian Li seems a bit easier to use but is more expensive.
The GD08 and the C60 both look good if you look at the front, only the Lian Li looks good from the side (->see WAF).
Neither case has good fans.
How many hard drives and which size (2.5" vs. 3.5") do you want to use?
I'm going to retire the last 3.5" drive in my desktop soon. In a HTPC I wouldn't want a single 3.5" drive. Installation of 2.5" drives is easier in the Lian Li and it fits 6, Silverstone only fits two 2.5". The Silverstone is sturdier and if you must (re)use 3.5" drives it will be quieter.
I would recommend a SSD (Intel, Crucial or Samsung) for the OS and a 1TB 2.5" drive for storage. WD makes a 2TB 2.5" drive, the height is 15mm instead of 9.5mm for drives up to 1TB.
Both are pretty big, which is good because you can fit a big cooler.
Noctua NH-L12 Low Profile CPU Cooler
Noctua C12 and C14 fit.
A Scythe Grand Kama Cross fits, keeping the fan on top only makes sense in the Lian Li with the top fan hole open. You can put the fan in the side of the case so it blows across the heatsink.
Seems like a no-brainer
No, neither case is suited for a fanless PSU. A fanless PSU needs room above for the hot air to rise. Get a Seasonic X-560 instead, the fan won't start until you run a game (or stress test both CPU and GPU) and will be quiet even then.
Scythe Slip Stream 140mm ??
I use Slipstreams, too. Noiseblocker NB-eLoop
look interesting, 120mm only for now and no reviews out yet. 140mm version will come out next year.