While I like gardening, unironically advising people to grow their own food to cut costs is just bonkers.
It takes months to grow anything, and given the limited space, you can't grow much anyway. You'll be lucky to grow 20€ worth of food on your balcony while spending hours doing the gardening. That's not cost effective.
You can get away with very little supplies, actually. Basically just a small shovel, the rest be salvaged.
Pots can be made from old plastic bins/containers, soil/fertilizer can be made from food waste using worms, seeds can be made from surprisingly many fruits/vegetables. Pumpkin seeds are right inside the pumpkin, potatoes and beans can be put right into the soil, even tomatoes can be grown from store bought ones.
And while it's a really cool hobby: you're right regarding the cost effectiveness. Unless you happen to have a significant plot of land, it won't make a dent in your grocery bill.