Remember, SAFETY is key….
Yes. Do not skimp on the PSU. The pedal board itself is an inconsequential rack of metal you will never even notice again once the pedals are on it - go cheap with it instead and save the money for a better power supply.
The Zooms all claim to require their own specific adapter (the Zoom AD-16). Not sure if there is anything “special” about that one vs. a regular 9V 500 mA adapter or if it is one of those “if we say you have to use ours then we get to make two sales” situations.
I was on that very page a couple days ago and got a chuckle out of the one star review at the bottom.
I think they just say that out of caution so folks who aren’t aware of the appropriate ratings don’t grab an old adapter out of their junk drawer and have to make a warranty claim.
Most pedals will use a plug with a center negative barrel, but not all, so that’s another thing to look out for. I had to order a new cable for my power supply (cioks dc7) because the cables it came with had right angle connectors and they wouldn’t fit into my zoom pedal due to the input being recessed.