The first thing we need to take care of is aeration:
The reason is, even if you do everything right and add only INORGANIC components to your nutrients solution; even if you use non-transparent containers... there still going to be organic molecules in your system: roots produce them. And it can become a substrate for someone we do not want: fungus or bacteria.
While if we aerate the solution, they are being supressed.
Compressor is not the must. There is a hydroponic method, called after its author: Kratky. In two words, we place root in the solution... and that's all. No aeration. The trick is to make sure that the liquid only covers lower part of roots, while there is an air gap between the surface of it and the lid of a container. This way roots can breathe.
However, it increases the risk of bacterial growth, especially in large tanks. Try planting something in a one liter yogurt container, add nutrients and use no aeration. Few days later you will see the thin film of bacteria at the surface of the solution. By the way, if you allow them to grow out of control, they will smell, and so will your appartment.
I use ceapest aquarium pumps available: their power is more than enough. By the way, i hope you know how to work with wires, outlets and so on; if not, you better learn first. For example, my outlets are located in such a way that even if I overturn a container, there will be no shor circuit.
Pumps vibrate, it means they are moving and can fall off the shelf. I use tape to hold them in place. Look at the picture above, pumps are taped to the shelf.
Note also that they are AQUARIUM pumps, they are more or less water proof, also they have rubber "feet" so even if the surface is wet, they are lifted and therefore safe.
By the way, when you grow micro greens, you do not need aeration: the depth of a tray is low and air can get to the roots by simple diffusion. However when you grow, for example, nut, it can create smell. Below I explain what to do.