My favorite hanging method is making a French Cleat. Take a piece of 2x4 and cut it down the center with the saw at a 45 degree angle. Attach one piece to wall, and one piece to item to hang. Very sturdy, and great for light weight all the way to heavy items.
When using 1/4" material I use #8 x 7/16" slide screws, typically used for mounting drawer slides. They’re a coarse thread screw with a super fine point for easy installation, no need for power tools, but they work well if you do. In most applications, the screw point doesn’t penetrate completely through the mounting hardware and material unless you’re using your super-kung-fu-grip strength to tighten them down, but if you find that they still penetrate the material (4-5mm materials), you can use one screw to start the hole then remove it and finish the installation with a screw that’s had the tip ground down. And yes, I’ve had to do that before when using a 4mm thick plywood panel for the side of a cabinet.