This will keep you busy for a while:
You are making me think, congratulations, I think eels like caves you can make with live rock, I always run a skimmer, hang on, or in the sump, it just removes waste from the water before it pollutes it. “But” you can run cheap with even a under gravel filter, or a sand bed which I don’t understand, and a mechanical filter.
It just strikes a nerve you replace all of that with a good skimmer when you get tired of changing water, the point, after a while you just buy a skimmer, a Prizm from Red Sea is about 100 dollars online good for up to a forty gallon tank.
Technically you are creating a healthier environment. The water is normally RO or distilled for evaporation and water changes. If you want to forget all that,...
The public water supply is alright. They have to spike the water with chloramine and chlorine once and awhile which you can remove with carbon, or an additive, get it to the right temperature something like 78-82 degrees, salinity 1.22 to 1.24 (fish is 1.22, reefs most go 1.24 and above). If you have animals from the right Ocean (Pacific for example) 78-82 is good. There are some salt water species from the Atlantic Ocean which from experience "never" gets past 72 degrees.
I started before wet/dry sumps where created, just had mechanical filters and under gravel filters, they were cheap and got the job done. Did not know what RO was. So it could be as simple as a mechanical filter with some type of biological filter (bio wheel for example), any light, and water changes with at least chorine removed. You can use any kind of lava rock, instead of live rock, eel with love all that.
Almost, forget, everyone agrees you have to cover the entire tank, anything that does not rust, "and" you need to add a "cycle" product to build up your biological filter in 2-3 days. Google "Nitrification Cycle".
So you have:
[*]
Light
[*]
Tank
Salt mix
Biological filter
Mechanical filter (which is replaced by a skimmer)
[*]
Salt water test kit
[*]
Heater
[*]
Hydrometer (measures salinity)
Something to monitor temperature
Place for the eel to hide like a cave
Or:
You buy live rock you need better lights (10K and Actinic 03 very common), I want purple Coralline Algae I did 20000K and Actinic 03, You should have a skimmer, use should use RO or distilled water (it adds up fast).
Consider what it cost to do the setup twice, in a pet store, and on the web.