Plants grow in air, not in soil. With a passive deep-water culture system you do not need to add air through an air stone-pump. You simply maintain an air space.
Start your seeds in the smaller two-inch net pots. I suggest using a mix of perlite (80%) and peat (20%) to start your seeds. You can use these net pots in the covers of your bucket, tote or PVC tube. You can also transfer the net pot, plant and all, into a wide-lip basket (WLB).
You can transfer your net pot seedlings into a WLB once the root system has grown through the openings on your net pot. Before placing your net pots in the larger WLB, add about one-inch of the perlite/peat mix to the bottom or the WLB. Set your net pots into the WLB and back fill the remaining space with perlite or LECA (clay pellets). This supports the net pot and seedlings.
Add your nutrient solution as per instructions for the brand of hydroponic fertilizer you are using. Your nutrient solution should touch the bottom of the WLB. This maintains the essential air space, without having to add additional air.
The perlite/peat mix that you added to the bottom of the WLB will draw up the solution towards the root system. As the roots develop and the plant grows, the water level will drop and the air space will become larger. Not a problem.
As long as at least one-third to one-half of the dangling roots are in contact with the solution the system is basically maintenance free. The air space is maintained. The roots are extending beyond the WLB. The plant should be thriving.
Note: If you are using the net pots without the WLB, have the nutrient solution touch the bottom of the net pot. This will maintain your air space.
Initially, the nutrient level touches the bottom of your net pot or wide-lip basket.