Maybe fractionally higher power consumption, and perhaps you'd need a GPU for it, but if both ends have really decent internet, that could very legitimately work.
Make one of these and you'll end up with a lot of money.
It's tricky. You could for example pick seL4, but then you have no router. That could be interpreted as an amazing opportunity to make a new stack, or a feat significantly less interesting and more strenuous than climbing Mt. Everest.
Then on the hardware side, do you pick x86 (complete with firmware that lets you use fallthru to ring -2! \o/), ARM, MIPS, or what? This is a question I've no idea how to answer.
Also, heh, I'm reminded of this:
1. Search Shodan for JAWS/1.0
2. Take one of the results, go to the IP[:port], append "/shell?" and a command, eg "/shell?ls"
3. Try running "whoami"
4. Go back and look at the number of results
5. Visit the IPs normally, and learn that these are DVRs, for security cameras; alternate between dying inside and reattaching your jaw.