If you go with ROCK, just a couple of things:
Technically, the Intel NUC is the motherboard for it. The CPU is certainly good enough, but this might install just a bit differently than a typical NUC. I wouldn’t worry too much about that, but know it could be the case. A lot of people install ROCK on a lot of other motherboards (see “Tinkering” section).
You certainly need to upgrade memory to SSD for the ROCK OS.
I’m pretty sure the DVD drive will be inoperative with ROCK. But you can now plug in a USB CD drive if you need to rip CDs.
What are you calling ‘cheap’? Once you add in the cost of the SSD (~$100) and some RAM, a similar NUC might be comparable in cost.