How do I pick an inductor(s?) for an LC filter on a power rail?
I can't read your circuit too well, but I'd suggest the following course of action. 
Figure out your current requirements - this will influence the physical size of the inductor, as you will need a larger core to prevent saturation as more current gets pushed through the inductor. 

Next, determine the transfer function of your filter in the frequency domain. Use this to draw a bode plot by hand or using matlab. This will give you some intuition about what frequencies get cut off as you change up your values.