I believe the Uno will clip right into the holder, without the need for any fasteners. At least that's the case with all the boards and shields I own that use these holders, and I have 7 of them.
RWagner:
there is not any information on the product page under Documentation about what size machine screws should be used.
It's M2.5. The length will depend on what you want to do with it. The distance from the top of the Uno's PCB to the bottom of the holder is 8 mm.
RWagner:
Also, it seems to defeat the purpose of protecting surfaces from the metal points on the bottom of the Arduino, by having the metal screws protrude on the bottom of the holder.
To me, this is not about protecting surfaces from the Arduino board, but about protecting the Arduino board from damage by getting electrical shorts from any conductive objects on the surface. For example, I often end up with a lot of cut off component leads on my workbench. If you power an Arduino board while it's sitting on a stray cut off lead, it's magic smoke time and you get to buy a new Arduino.
RWagner:
There may even be some plastic caps for screws to put over the metal parts when using this, but the Documentation gives no help about that either.
You can buy nylon fasteners. I often use them for other types of boards that have been designed in a way where the head of a metal screw can make electrical contact with components on the board and increase the likelihood of shorts. The nylon standoffs make nice feet for holding those boards up off the table to prevent shorts, but the nice Uno and Mega-style holders Arduino makes provide better protection.
CrossRoads:
The holes in the Uno board are 3.2mm. 2.5mm or 3mm screws/nuts should work.
The holes on my holders are all smaller than the holes on the board. 3 mm screws won't fit, though you could probably tap them to M3 if you wanted threads.
CrossRoads:
Getting a nut next to Aref/SCL/SDA header is a challenge.
I think this is actually the reason for the holes being M2.5 instead of M3. The head of the M3 screws doesn't fit in the space next to that header, but the M2.5 screws I have work fine.