< £125 Hit-around PC

Hey Tek Syndicate Forums!

I wanted to have an always-on PC that would be able to record Live TV, using a PC TV 292e USB Tuner. I'd also want it to mess around with a LAMP stack, and potentially use it as a "normal" productivity machine (LibreOffice, web browsing and development).

Requirements

I need a system that is:
- Small (enough so it can fit within a 30cm x 30cm (11.811 inches by 11.811 inches) space)
- Cheap (< £125)
- Can be left on all day unattended
- Can handle recording and playing back HDTV (possibly at the same time)
- Support Linux / Kodi / OpenELEC

Research

Intel NUC NUC5CPYH

So far, I've narrowed it down to the Intel NUC NUC5CPYH.

According to some blogs, such as NUC Blog, it can handle 1080p playback using HEVC, but I don't know whether that is applicable.

According to the same blog, it consumes around the same power as a light bulb.

AMD Athlon 5350 APU

I've looked into AMD builds, such as this fanless AMD Athlon 5350 APU build which would come just within my budget.

I don't think I can go for it because:
- Not many places stock picoPSUs, and they charge an arm and a leg for them
- If I swapped out the power supply, it would make the case larger
- Linux on AMD APUs apparently suck (although the review is old, current kernel version is at 4.4, and I haven't seen any new reviews or benchmarks).

Raspberry Pi 2

I already have a Raspberry Pi B+, and I simply can't get it to work.
I've ruled this one out because:
- RPi B+ is not powerful enough to even run the file server efficiently
- Kinda janky, got to buy a USB hub just to power the TV Tuner
- OpenELEC performs badly (from my subjective experience)
- I'm not sure investing my money into the RPi would be a great idea in the long-term

Parts already obtained

I already have a keyboard, mouse, monitor, and storage (I've got a spare 2.5" hard drive), as well as the TV tuner.

Can you guys recommend me anything that might match?