I think you need to start at the basics. KCL, KVL, Mesh and Nodal Analysis. Using a breadboard, wires, power supply, meter and resistors you can accomplish this. first, look up those terms and then design circuits based on those terms (circuit in series, circuit in parallel, circuit in both series-parallel) and then use the proper equations of ohms law, KCL, KVL, Mesh, and Nodal circuits. That is pretty much the base of everything. As for approach, I suggest drawing random circuits and creating random numbers for voltage, resistance, and current. Then when you understand the terms I listed mixing it up so that you do the math first, then verify it with physical circuits second. That is my opinion and I know others might disagree but I feel having a strong grasp of the math is equally important as understanding the physical side to circuit design. Once you are comfortable with that evolving from there into more complicated stuff. IMO a understanding of KCL, KVL, Ohms Law, Mesh and Nodal processes is imperative to understanding what a physical circuit is doing.
All this requires is a breadboard, PSU (variable of course), wire, resistors and a DMM to check volts and current, sometimes resistance.