Help: Radar Sensors
Take a look at the Skolnik radar book (Introduction to Radar Systems) for a very basic intro. You can detect many, many things with radar. If you want fast/cheap sensor, you can use a pulse radar and detect the return (backscatter). The amplitude tells you about the scattering characteristics of whatever you're detecting, the delay between pulse and return tells you distance. I dunno what kind of scatter you'll get from wood, so dunno what level of power you need for the pulse.
You can tell all kinds of other info from a doppler radar but you'll probably need more sophisticated circuitry. Doppler is good if you need to know speed.
There are many, many other concerns depending on what you need. Antenna matters a lot (more directive if you want more range), LNA is huge if you're dealing with very small received signal (not likely here but who knows), etc etc. Take a look through Skolnik for some real basic questions/answers.