Hello! I have a nice 1/2 barrel setup (or had until raccoon at my fish...A story in another post) . Here is what I had that worked perfectly in US Zone 7.
I had 2 half barrels. Both PVC lined. One barrel was on the ground. The 2nd barrel was on our raised deck (maybe 1.5-2ft at most). The top barrel had a handmade wooden spillway . For the spillway I had to cut a few slats in the barrel, folded liner into cutout, siliconed (aquarium grade) inside the cutout on top of the liner, squeezed in the spillway (the tighter the fit the better), added a few screws to secure, and siliconed inside the barrel on the liner and edge of the spillway so water could not seep in between. There was also old-timey hand pump on a wood shelf on top of the deck barrel. Water would start in the top barrel, pour into lower barrel via spillway, pump back up (will explain that next) thru tubing into the inlet of the old timey hand pump on the top barrel and just keep recirculating that way. So in reality I had 2 "waterfalls" for aeration; one into the top with the hand pump and one into the bottom via the spillway.
Since I planned on fish, I had to DIY a filter system and here is what I created. I went to a garden center and picked up a small submersible pump rated for 350 or so gallons. I found a clear tub with a lid that was approx 7"x5"x6" (or whatever will fit the pump you buy + room for filter media). It was actually a container my doggy treats came in! I drilled a series of 1/2" holes on the bottom of all 4 sides for water intake. Inside I laid some quilt batting to above the drilled holes for mechanical filter. Then I laid in a layer of lava rock for biofilter. Pump was set on top of lava rock. More lava rock laid on top of pump. Then another layer of filter media. You can probably avoid the top layer of filter media if your lid is pretty water tight. Mine leaked a bit so I added the additional top layer of filter as a safety measure for my pump. I drilled a hole in the lid that was just big enough for my tubing (1/2"). Slid tubing thru lid and attached to the outlet of my pump, then replaced lid. Tubing went from filterbox pump, to the bottom of my upper barrel. On my upper barrel I drilled a hole in the bottom for a 45deg 1/2" barbed fitting to fit snugly into (this did not need to be watertight since it was under liner). Hose was attached to outside barb and hose clamped. Another piece of hose was clamped to inside of barbed fitting and another hose clamp. This hose was then attached to the inlet of my hand pump. PVC liner was placed over the tubing in my upper barrel, running tube along inside curve and in a fold to keep weight of water crushing it to a minimum. In my particular instance, I had to cut a small slit in the liner above the waterline, under my pump shelf to get the tubing to my inlet port of my hand pump.
This setup ran perfectly for 3 years. I had 8-10 med-large shubb's & sarrasa's that entire time. I cleaned the filter out whenever I noticed the waterflow decrease by half by just replacing the batting in the filterbox. Maybe 4x per year at most. I kept up to 5 fish and plants (water iris, and floating plants) in each barrel during the summer. During the winter all fish would move to top and iris to the bottom. Pump-filter moved to the top and water lever dropped just below the spillway so water filtered only the top barrel. A shorter hose put on pump so water created more of a waterspout to keep aeration. Handpump put away for winter so it did not freeze and crack. Bottom was kept with only enough water to cover the plant rootballs for winter. Water in bottom was allowed to freeze. Kept the top ice free with a small submersible aquarium heater in winter. Water temp maintained around 60 all year. Fish fed normally and grew about 1-2" per year. I did one large spring cleaning per year when I was ready to re-start bottom barrel.
For upkeep I used a dechlorinator whenever I did water replacement for evaporation. When I did filter cleanings, I would do a 30% or so water change. I also used an aquarium startup product (bacteria replacement) whenever I did a filter cleaning/spring cleaning. When doing filter cleanings I also used an aquarium vacuum to get most of the gunky gunk that accumulates at the bottom of the barrels. At spring cleaning I would do a 50-75% water change depending on how water looked. My water stayed pretty clear (I could see bottom) all year. Only exception would be during the spring algae bloom which would go away after a few weeks. When I was impatient I tried a small UV clarifier for the algae bloom, but it did not seem like it did anything but cost me $...
I was probably pushing the limit of my filtration with my fish load since the fishies we so big (up to 7"), so I would be wary of that and plan on filtering on how big fish will get, not the size they are now. My water specs always were good with nitrite/nitrate/ammonia. I would check them often when I started, then less once everything was established. I wish I had taken pics of that old setup!
I had very good luck with that setup and wish you the same (except for the raccoon part!) ;-) and sorry for the long post!