I am using an external filter as well
If your tank has a stand or shelf under it, you can hide the filter there
I have mine standing next to the tank, because there's a wall on the cabinet under xD Anyways, be sure to get a filter that can pump at least 1200 gallons/h. Even bigger than that would be better! External filters can usually handle a larger bio load and a bigger amount of water, so they're usually recommended for tanks bigger than maybe... 60 gallons, I believe. But there are smaller external filters available too
They basically look like this:
With hoses connected to the upper and lower outflow respectively intake. The one on the picture is the one I've got, but they are all basically the same, just with different looks
It's sometimes good to combine filtration in your tank to make it even more efficient! I've got a smaller internal filter as well, rated for a 56 gallon, but combined with the external filter it works very good!
You should try finding a pet shop with lots of knowledgeable people and ask for advice about filtration there!
And I would, if you can, give away a few of those fish. At least the koi, because they will outgrow the tank in a minute! Your 120/125 gallon can only support a maximum of 12 fish. Unless you'd be checking the water chemistry and doing regular water changes when needed. But try to decrease the number of fish to maybe 14-16 or something
With good filtration you can pull that off!