Help choosing coefficients for a simple FIR filter to extract DC component I am a beginner in design of digital filters... I have just completed Coursera's Linear Circuits course!

I have a signal which is sampled at 50 Hz where the DC component has a value of 800000 and there is some noise with a standard deviation of around 200. The DC component should remain constant but it may change very slowly over time.

I want to design a simple FIR filter to obtain the DC component: would a simple weighted average algorithm be most appropriate? How do I go about choosing suitable coefficients?
MA is almost never a "most appropriate" algorithm (it's only advantage is simplicity). My advice is to choose Gaussian filter which has least possible group delay. Calculate its coefficients keeping in mind that cut-off frequency of a Gaussian filter is $$f_0 = \frac{1}{2 \pi \sigma}$$
Estimate which variances of low frequency component you'd like to preserve in your application, which are acceptable to be attenuated to 50%, this will give you desirable cut-off frequency.