I used to run OH on my HP microserver, together with a lot of other services. Later on, I just wanted to have a separate machine for my home automation/security. I just went with debian on an old eeepc I had left gathering dust during the last 3 or 4 years. It is perfect for that use.
If anybody is going the PC route, I would suggest them to use an old laptop. Even a 10 years old one would be more than sufficient to run OH, if the O/S is Linux, of course. Also, laptops consume considerably less power than full-blown PCs (although not comparable to a rPI), and if the battery is not dead, they have an in-built UPS. And keyboard/screen for local use, if need be.
Whew, a OH box does not have to perform I/O like a fileserver has to. You don’t need to care about USB3, SATA or TRIM.
A RPi2 or 3 is fine. If you really wanna go with an Odroid, better check out the C2. More bang for the buck, you can even run a 4K capable media server in addition to OH if you want to.
And as - surprise - you’re not the first to raise this topic, check out this thread for an older discussion. Also check out the link at the end of this thread for a comparison of single-board computers.
On SD (and even SSD!) corruption, check out this post.