Lolwut? While the choice of ITX mobos was always sparser than (m)ATX ones, every major manufacturer cranked out at least one model (if not more). You should have quite a few options to choose from.
My HTPC runs on an Asrock FM2A88X-ITX, and I'm quite happy to recommend that board if you can find it. While it was quite pricey, it has all the shit I'll ever need integrated onboard. There's also the very similar newer model, A88M-ITX that should be fine too. One major advantage of both is that they have the CPU socket near the center, leaving more place around it to install a larger cooler in a cramped case like that Chieftec. And the vent in the side panel is then right over the CPU, letting the cooler suck fresh, cool air from the outside.
There's nothing to support here. Wireless and sound are provided by standard, ubiquitous chinkese chips (Realtek or Broadcom? I don't remember..) and all the other interfaces are straight from the chipset. Everything is perfectly supported by mainline Linux kernel. Firmware updates can be done straight from the UEFI, you don't need any Windows-only flasher programs.
This is not an expensive 1337 [email protected]/* */ mobo with obscure RAID controllers or "Killer" network cards that have drivers only for Windows. Everything should just werk.
Bear in mind that the TDP is calculated for the worst-case scenario with all cores (including the GPU!) running at full throttle at the same time. If you load only two cores of the quad-core chip, the power draw will be no worse than on the dual-core part. Basically, you only pay the extra watts when you actually use the extra processing power.
And even the shitty stock cooler can keep the top-of-the-line A10's temps in check. At worst, it will ramp up the RPM at full load and sound like a fucking hairdryer, but it will hold out. If you don't like the decibels, you can either get a better cooler, or configure the power governor in the kernel to limit max clocks under all-core loads. Or just don't run anything heavy when silence matters.
Not by much though. All of those chips are dirt cheap today anyway. I don't think it's worth sacrificing this much performance for a few measly bucks, especially if you plan this machine to hold up for many years. Get a quad-core if you can.
The APU contains a GPU, yes, however the video outputs available are determined by the mobo.
Then check out other shops. And fleabay. The Internet is full of offers, and processors are tiny and cheap to ship.
Both are total overkill. If you don't need any addon PCIe cards, it would be a waste of space not to go with a more compact ITX or at least mATX case. Also look for slim cases with half-height expansion slots. Almost all PCIe cards these days (except graphics cards) are half-height anyway, so you won't realistically lose any expandability.
Your build will pull below 100W in total. You don't need a 450W PSU.
Get faster RAM, preferably DDR3-2133. It's only a few bucks more, and the iGPU will massively benefit from extra bandwidth. And get two sticks for dual-channel operation.
I strongly recommend an SSD as a system drive. You can get a 240GB OCZ Trion 150 for barely $10 more than that HDD you specced. 240GB ought to be enough for an office/web machine.
And, for the love of Kek, if you do need an HDD for bulk storage, do NOT buy a WD! These drives fail left and right at ridiculous rates. The only HDD manufacturers with a decent reliability record these days are HGST and Toshiba, and HGST drives are ridiculously overpriced - so Toshiba P300 it is.
Sure, no problem. With some more conservative distros you might have to fiddle a bit with kernel config to make HDMI audio work, everything else should work out of the box.
The first APU generation to have the PSP is the 7xxx. All the 6xxx and older are botnet-free.