A wooden water wheel can be an affordable data-gathering device, but you should plan on ending up with a metal wheel.
In a location that experiences lengthy freeze-over when you want to get power from the wheel, I recall an old fieldlines post where someone was attempting a VAWT underwater, with the generator above water at the end of a short pier.
The leading edge was shielded from flow, and the trailing edge was driven by the current. The power shaft ran through a protective pipe that was located at the level of the ice cap. I haven't heard how it turned out, or what type of lower shaft bearing would be best.
The rim speed of a wheel will probably end up being about 90% of the water flow speed. To spin a generator fast enough to get decent power, you may need to use a "gear-up". A car differential "might" be able to be used as a 4:1 RPM increaser if spun backwards. If greater gear-up is needed, toothed rubber belts and chains can be found, but they are more expensive and have to be maintained and replaced when they wear out.
Before steam engines, breast-shot/hip-shot water wheels were the staple of many factories. If more torque was needed to get adequate gear-up, the wheel was made wider (Google DuPont gunpowder water wheel). If you make a VAWT underwater, you will be restricted to depth of stream at lowest annual level.
Depending on conditions at location, you may find wind is a better first effort from a cost/effort Return On Investment (ROI)