Precision Full-Wave Rectifier: Why is the signal's biggest magnitude at DC?
The Fourier series of the full wave rectified sine wave is (from here):



The DC component has magnitude 2A/π, while the first AC component has magnitude 4A/3π. So that's why mathematically the DC component is largest. You'd expect a large DC component because rectification makes the whole signal positive.

You don't want to filter everything about 2 kHz because then you'll just end up with a sine wave again. All the frequency components are important to the shape of the curve, so you should keep as many as possible. Because of the Nyquist limit, you'll want an antialiasing filter to remove everything above half your sampling frequency (and a bit more for safety).