If you definitely want to go with a Prodigy, then it's likely one of the coloured versions (ie not Black) is going to be quieter, as they come with a solid front panel rather than a mesh section.
Just as a quick FYI, a Prodigy wouldn't be my first choice as a HTPC in a living room, because it's not the easiest thing to fit into an entertainment centre/shelving (front panel on the side doesn't help) and on a carpet it can have quite a nasty wobble.
CPU cooler -
You can just use the Intel stock cooler, but if you want to try to keep the noise levels low, you'll need to be careful here. I'm fairly confident that the largest tower cooler you can fit on the motherboard you've selected will use a 90-92mm fan. Many popular tower coolers (which do fit in the Prodigy) like the Hyper 212 Evo, use a 120mm fan, and I'd be very hesitant about suggesting them as they will struggle to fit on the motherboard due to the CPU socket location.
Here's a video using that cooler+motherboard combo, and you get a (bad) look at how tight it is, so I'd definitely suggest sticking with smaller coolers.
Coolermaster Hyper 101, Hyper TX3, Arctic Freezer 13, EVGA ACX ITX cooler, Xigamatek Loki. Lots of options, most of which aren't too expensive and should in theory run a bit slower than the stock cooler due to the heatsink.
Graphics card
Pretty much every manufacturer at some point will claim their card is the quietest, and in every benchmark you see different results because sound is such a hard thing to measure with any kind of objectiveness.
You have loads of space so you have a lot of options. The MSI, Asus, EVGA and Gigabyte versions are all supposedly pretty quiet, and you can also adjust fan profiles in software to make them run quieter by slowing down the fans (at the cost of increased heat).
PSU
Fanless PSU isn't really an option in a Prodigy, as the closed off PSU box means it won't be able to get rid of any heat- most fanless PSUs specify that you install them with the mesh section facing up, so that they can vent. You are also limited to 160mm length in PSUs, so be careful that whichever you pick conforms to this. I personally use an XFX Core550 in my Prodigy and I have no complaints about noise levels, but it's a fairly subjective thing. Usually it's not the noisiest component in a build, plus it sits at the back, it's probably not something worth worrying about hugely.