This type of connector, which is designed to accept bare wires, is called a terminal block, specifically a wire-to-board terminal block. They're a cheap way to make non-permanent connections that don't need to be easily broken and re-made.
The specific type you have here seems to use screw terminals, where you insert the wire and then twist down the screw until the wire is firmly held in place. You should not rely on this connection mechanically, but it is a good electrical connection. If you use a power cord with this, I recommend applying some sort of strain relief so that any accidental tugs on the power cord don't cause problems.
While they aren't necessary, it may be useful for you to put ferrules on the ends of your wires, which will help keep the strands together and, to a minor extent, help prevent the wire from breaking if it gets pulled out. As this requires a crimp tool (which many amateurs don't have, in my experience) I'd like to make it clear that this is by no means a necessary part of the connection. It just improves reliability.
As for what power supply to use, there are other questions on here with answers that cover that much better than I could.