A lot of questions here, I will try to weigh in on the ones that I can answer.
Farm raised fish have the potential to be healthier than ocean or estuarine commercially harvested fish because the farmer can control the water they live in.
I will warn you that many commercial fish feed pellets are made with fish protein harvested from pelagic schooling fish such as menhaden. It’s all well and good to raise fish in clean filtered water, but if the food you’re raising them on is high in PCBs or heavy metals, guess what? Your farm raised fish can have levels of these toxins as high or higher than those of ocean-caught fish.
A subsistence fish farm is a great idea as a hobby, but I highly doubt that you can start from scratch and grow your own fish economically, i.e., compete with commercially available frozen fish fillets.
Several people have tried combining aquaculture with hydroponic farming (a nice arrangement because fish waste serves the role of fertilizer) with limited success.
The best choice of a fish for farm raising depends on your climate and pond setup, as well as your personal taste for the finished product, but Tilapia are a good-tasting and fast-growing fish that are successfully farmed in warm climates all over the world. Unfortunately, they cannot survive water temperatures below about 50 degrees F and their rate of growth is much slower at low temps. This is why U.S. fish farmers in temperate climates typically grow catfish or specialty cold water species such as salmon or trout.
Costs to heat, cool, treat, or filter water year round are probably prohibitive in a small subsistence setup. Of course, if you have too many fish in a small pond with no natural source of food, you’ll also have to add supplemental food, which can be expensive as well.
On the other hand, if you have access to or can build a small impoundment 1/4 to 1/3 acre or more, it is definitely possible to grow and harvest your own freshwater fish with little to no work at all - just stock the pond with an appropriate mix of species and let nature take it’s course. I work on the east coast, so I do not know which native CA species would be appropriate for aquaculture, whether your climate is suited to Tilapia culture or whether you’d need any permits to carry out this plan.
Lastly, any fish, whether farm raised, recreationally caught or store bought may contain potentially harmful levels of PCBs or heavy metals. Your best bet is to avoid eating fatty species of fish and remove the skin and fat of any fish you eat before cooking. IMHO Women of reproductive age and children should probably limit their consumption of fish as a general precaution.