Barrel style simple system?

I have an idea that might be completely wrong, but didn't know if anyone has tried anything like this before.  My idea is to dig a hole in the ground to inset a food-grade plastic barrel with the top cut off as a way to 1) grow some choice goldfish for ornamental pond stocking, & 2) supply me with a steady supply of fish-waste water to fertilize a garden.  The below ground depth would allow for overwintering of the fish below the freeze line I believe (plus we have mild winters most years).  My question is this, in a spot without electricity, would it be possible to use a cheap portable solar panel to directly run a recirculating pump or aquarium style waterfall for aeration, or something similar?  The idea is that I'd be taking out about 10 gallons of waste water per week, siphoning it from the bottom of the barrel (where the waste collects), & replacing it with fresh unchlorinated water, so filtration isn't super important to me.

I'm not real savvy when it comes to how much electricity a small solar panel needs to produce, how much a pump needs, or if I can use rechargeable Li-Ion batteries, etc.  I'm just wondering if there's any advice you all might share about this, or links to similar projects that I might glean some knowledge from?  Thanks.

You'd have to test your system for proper equilibrium, but typically, air pumps with air stones need a lot less electricity than recirculating filters (around 1.5 watts for a small one to fit a 16 gallon tank). That's what we use during power outages. It also seems to be the aeration option of choice for large ponds.

That said, I haven't been running a fish tank outdoors, but I have two of them indoors, and I do have to say that they are tricky to get stable. Sunlight tends to produce lots of algae (because of the yummy nitrogen content) or blue-green cyanobacteria. Fish in small quarters are easily overfed or overstressed from the slightest thing. I find that it's been an amazing experience for my kids to learn how fragile an ecosystem can be and how to be good stewarts of nature, but it requires care and frequent monitoring to be able to react to problematic situations.

(I hadn't realized that taking care of fishes was to become a kind of medieval fish doctor: all the illnesses have names like "dropsy" which can refer to any fungus/bacteria/virus/parasite/injury, and treatment can be any of several cure-alls. So you try whatever you can to save them and fail 75% of the time, as our backyard fish cemetary testifies. )

I do have many years of experience with indoor aquariums, fish illnesses/medication, and water quality.  So, I have that going for me.  My thinking is to have about 50 gallons of water in the barrel, and a wooden top cover with a concrete block to keep the critters out.  I'm not too concerned about the algae since I'll be taking about 10 gallons a week out of it to use as fertilizer.  I have dealt with dropsy, ick, fungus, & stress induced illnesses in fish before, and sometimes I found myself spending lots of money to save/hear them.  Good life lessons for children though about ecosystem balance.  Some of the best planted aquariums I've seen have found a balance in all aspects.