Cheap's relative in koi!!! You can get away from the third of the pond rule with modern media and ideas, but bigger is better. As far as the fish are concerned it can't be too big, but real life obviously affects that!
From what I gather, you've already dug and lined the pond?
If this is right you're going to really have to use a pump fed system with the pump in the pond feeding a filter that then empties out into the top of your waterfall. I'd suggest a similar system to the one I'm using on my quarantine set up, only scaled up. i'd have the pump in the deepest part of the pond pumping water up into the filter.
The filter itself I would build from two containers with the first static K1 and the second fluidised K1. That link I posted before is the basics of DIY K1 filtration (they call it active bed media, but it's the same thing).
The first will be your mechanical filtration (though it will act biologically too) and will need to be regularly cleaned. Fortunately the huge advantage of K1 is that this means stirring it up, ideally with an air pump.
A static K1 chamber simply needs to be a container that stops the little pieces of the K1 media flowing out! As it floats at the top the exit pipe, with slots cut in to strain the media out, needs to be at the top too. My empty QT filter looks like this,
The K1 media will float around the upright 4" pipe and strain out all the debris while bacteria will grow on the media too. Notice too that I have a drain in the bottom of the tank (the red cap). This chamber will catch all the dirt from your filter and this is the bit you'll have to clean out as often as possible (It is dead easy so that's actually not a chore and the waste water can go on your garden).
For a small pond that will be all the filter you'd need, but for your pond I'd have that filter linked up to another container with fluidised K1 in it. This is a very similar set up, but the filter being is kept moving by adding air to the filter chamber. This really increases the efficiency of the filter and, best of all, it is completely maintenance free! The media moving constantly doesn't trap any dirt and cleans itself!
You'll be best to do a fair bit of reading before actually starting to build one. Try doing a search on google for 'DIY filters K1'
This is good thread from the US and shows the basic ideas too.
http://koishack.com/forums/index.php?showtopic=5007&st=0
I have just finished my filter and if I'd known about K1 when I desgined it I would have designed it rather differently! I will be retro-fitting it with static and fluid K1 next summer I think!