Yes you need +12VDC and +5VDC, and yes a computer power supply will provide that. There are other options you may want to consider. A quick search on Amazon found this
Meanwell supply that puts out +5VDC at 4-amps and +12VDC at 1-amp. This particular model may not exactly meet your needs but if you do a little searching, there are plenty of "industrial" switching supplies that are used in various situations that require+12VDC and +5 VDC. They are not uncommon and might be a little cheaper than a computer power supply that has extra outputs (PCIE etc.) that you do not need. I would not buy the cheapest no-name brand you can find. Look at Meanwell, Acopian, OMRON, SOLA, and Siemens.
It's an interesting ap[plication, and one that can benefit from the fact that the Octo has its own internal processor, and once configured, can run without an active USB connection.
Good luck!