Hey so the M.2 is just a PCIe x4 connection, with direct-to-CPU lanes (the X300/X600 are basically 'activator' chips for the onboard SOC, not a real chipset)
The PCIe x4 signalling is passed through to a PCIe slot, on a riser that has its own power input
-- This is achieved through a riser that directly adapts an M.2 slot to a PCIe slot (like those from ADT-Link, as well as numerous clones)
The X300M-STX is able to run on 12VDC, so that makes powering a GPU and the board with the same power supply relatively simple, however the X600M-STX requires modification to work on 12VDC
You can also run the motherboard on 19-20VDC and then have an adapter to reduce that down to 12V for the GPU, or even have two separate power supplies (one for motherboard, one for riser & GPU)
The options for the actual power supply are fairly broad, but you'll want to make a decision early on whether you want internal or external, and whether you want 19V or 12V, as that will influence your design significantly.
Internal power supplies include things like Meanwell LOP series and clones
External power supplies you can use high current 12VDC (although connectors are often the problem here, as even 120W to the board means 10A on a barrel jack!) or a 19V supply and a secondary power adapter to reduce to 12V for the riser and GPU.
