There is no absolute cheap way to grow. Whether it be time, money or a combination of both.
You cannot make adequate hydroponic nutrients cheaply. I know because; I make hydroponic nutrients. I have to buy a minimum 5-6, 50lb. bags of nutrients; Plus, Many 5lb. bags of chelates for micro nutrients. Boron, etc, etc.
Cheapest way to go hydro is to buy a base nutrient system.
General Hydroponics 3-part, about 30-40 bucks for qts.
DutchMaster Advance A + B Bloom, Add Max, Silica, Zone. ) I use this now to measure side by side; Using my
"custom" mixes against commercial nutrient systems. Not bad or, too high priced, once you are set up. you use less of the additives 1 to 3 than the A+B. Around 50-60 bucks. Will last beyond one grow. Maybe 2. Depending on your consumption.
It will cost you more than 60 bucks to put together all the necessary tools, minerals, and monitoring equipment to control all of it.