Just type "passive hydro systems" into your search engine and you will get a ton of information of the various types. I use a passive wick system for growing lettuce in my living room. Nothing big and certainly not fancy, but effective. No wires or electricity. That said, an active system will probably allow for quicker growth. Because there is no circulation, as Bird McBride points out, you have to stir your solution. You could add an airstone if you wanted.
I have an ebb and flow system that I use that works great. Started with the basics and then added and modded where necessary. It is not passive, but not hard to set up. I have also used bubble buckets and DWC. These take a little more work than the E&F, but are still fairly simple to work with.
As for nutes, that is the sticking point. Any soil free hydro system is going to take some getting used to. The time between a problem starting and a problem causing damage can be minimal, so you need to understand how to read your plants. This is where you will need to research the most when starting. Don't let that scare you though. Having complete control how the plant eats also brings about the best rewards! Well worth the efforts.