Waterwheels come in four basic varieties, of varying efficiency.
Which type you can build is governed largely by the local geography...
Overshot waterwheel at Y-Felin
If you can build you mill on the side of a hill, and have a water supply from above, then you will typically build an overshot wheel or a pitchback wheel. You'll need a drop of at least 15 feet to do this. In both of these types, the water is admitted to the wheel very near the top. This gives the greatest possible distance for the weight of the water to do its work which makes these wheels very efficient. Ratings of 80% to 90% are possible. You can do quite a lot of milling with comparatively little water. The main difference between them is that with a pitchback wheel, the exhaust water flows away in the direction of the rotating wheel, whereas it flows away against the rotation of an overshot wheel. The pitchback also needs a slightly more complex water supply arrangement directly above the wheel, known as a penstock, to build up a small head of perhaps 2 ft. With the overshot wheel the water can simply be led from the millpond down a wooden trough (or launder) and straight onto the wheel - the speed of the water giving added impetus.
Breastshot waterwheel at Chalgrove
If you can only provide a head of water of some 6ft to 8ft your best bet is to build a Breastshot wheel. Here water is admitted to the wheel about half way up and it flows out with the rotation of the wheel. Breastshot wheels could be made very wide to increase their power output and, more than any other type, tended to be iron built wherever possible. The whole of the early industrial revolution was powered by enormous breastshot waterwheels. The wheel installed at Quarry Bank Mill at Styal in Cheshire (another National Trust property) is an absolute monster at 22 feet wide and 25 feet in diameter and weighing in at 20 tons.
Undershot waterwheel at Mapledurham
In areas with no slope of any kind to speak of, such as we find at Whitemill, the only choice is the undershot waterwheel. Compared with the other types this is horribly inefficient. Here the wheel relies on huge quantities of water, moving at considerable speed, to drive the mill. Such mills are usually built on substantial rivers - streams just don't have enough water. Typically, a percentage of the water in the river is diverted along a leat to the mill. Undershot wheels are normally quite narrow and have to fit very accurately within their channel to prevent the water from escaping round the sides.
As you look at the various types of waterwheel, you will also see that they tend to have characterisic bucket shapes. The overshot wheel normally having straight buckets set tangentially to the wheel, the breastshot wheel having heavily curved buckets, and the undershot wheel simply having straight paddles sticking out from the rim.