First off, they are filter feeders but NOT like you imagine. They don't take water through their body and remove the food in the process like a clam would do. Instead, the capture the food with their appendages and pass the food to their mouth for digestion.
When they first hatch out, they cannot feed as they don't have complete digestive systems until instar II stage.
There are many foods that they can eat, yeast, brown rice flour, egg yolk,(all micronized in a blender for at least 2 minutes) and live phyto and much more. To be practical, I start them off with live nannochloropsis and then switch them to spirulina flake/powder that gets blended in water for 2 minutes and stored in a pop bottle in the refrigerator, adding just a little multiple times a day is best. (Actually, because I grow in large containers I have built DIY pop bottle dosers to add the spirulina water over a 12 hour period)
Before I forget, DON'T USE AIRSTONES, use open ended air lines. Small bubbles can get trapped in the brine and suffocate them.
Aquariums aren't the best containers to keep them in as it's hard to keep the food in suspension. Ideally one would use a deep cone but for me the cost is too high for the volumes I produce.
Small quantities can be handled quite easy with pop bottle hatchers and then transfer them to larger containers for grow out. For me, the next size up was 4 L wide mouth jars that I sat on an angle so the air line had a better chance of keeping the food in circulation. Not the best but better than just a tank. Now I use 26g rubbermaid containers, still, placing them on an angle to have a low point for the air line to sit.
Brine cysts are known for harbouring nasty bacterial like vibriosis so it's best to sterilize them or decap them before hatching. Rinse them well at EVERY stage you remove them from culture water.
Depending on the density of your culture, you may have little work or a lot of work. Culturing in any MEANINGFULL density IMO is labour intensive and takes a number of times to get a protocol down that will work for you.
The best cysts to use are those stored in a refrigerator. Ones kept on a shelf many times provide low yields and even sometimes, no yield at all.
You might be better off buying live brine from livebrineshrimp.com.
My write up for brine can be seen at
Raising Brine Shrimp It might possibly give you an idea on how to tailor it to a viable method for yourself on a scale you want to attempt.