Slicer file available!

I suggest you to take normal PETG, which is very resistant and ensures water density. As you can see in the pictures and description, the plant tower is modular and stackable. The only thing you need are capillary cords. I used 3mm wide cotton cords. Place them as described.
After stacked, the whole tower is filled from the top. Approx. 450ml per module. When water drips into the reservoir, all modules are filled. 
Use clay pellets or something similar as a growing medium for the plants. This allows the roots to get oxygen while still staying moist.