Just putting a sump down there won't do anything, you still need a pump to lift the water back up along with plumbing and filter material for the sump. Also I'd use a much bigger sump for a 125g. I'd go for a used 55g tank or something personally. It will also probably need to drilled for fittings.
Do you mean AC110s? I would just get two of them for now as the pair will filter a 125g pretty decent. And you can get the pair for like $100 using the code from Dr Foster Smith.
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As for how/why a sump?
- Water pours from the tanks overflows into sump.
- Through filter material of your choice inside the sump
- out of the drain in sump into the pump
- pump then pumps it back into the tank
The amount of filter material you can fit in a sump is much larger than any normal filter.
The increased surface area for filtration results in less frequent cleanings and a more stable environment for your fish.
The large increase in water volume of the system also adds to stability as well as helping the temperature stay constant, larger the body of water the longer it takes to go up/down in temp.
Also if the sump is large enough you can put your heaters in it to keep the tank less cluttered.
Also if the sump is large enough you can do the water changes within it instead of probing all over your tank with a siphon tube. Plus it will need cleaned anyway because crap will buildup like it's supposed to.