Short answer: Choke you linked looks good for the frequency range typical from a switching power supply.
Caps: a 470uF before choke and a 470uF after.
If you are hearing power frequency hum (100 Hz, 120 Hz) then you will need to add a big inductor in front of all of that: L > 10 mH, or if not wanting such a huge inductor then use more capacitors. It might need a 20 ohm resistor in parallel to damp the resonant network...and this is low frequency enough to tune using Bela Scope. You can measure the power supply directly and look at it on the scope.
The best design method would come from knowing how much ripple & noise the power supply has, and then knowing how much it needs to be reduced. You also need to know the switching frequency of the power supply.
If you have an oscilloscope, it's easy to find out. Bela scope isn't likely to help much because you ideally need >5MHz bandwidth to capture the pertinent information.
In reality, the average guy doesn't have a scope, so we may have to make some assumptions. If you have an oscilloscope then just stack up filtering components until high frequency spikes go away and output ripple is <20 mV or so.
Here are the assumptions:
It's probable that a cheaper/noisier unit of 1A output likely has 47uF output filter capacitance. For a 1A supply at 50 kHz and nearly 50% duty cycle, ripple voltage will be theoretically close to 250 mV + some > 1MHz oscillations on the switching edges. But wait, there's more!
All in all we estimate 350 mV peak-peak ripple voltage.
Change in voltage on a capacitor for a constant current charge or discharge rate is this:
V = i*T/C
i = load current
T = charge or discharge time
C = capacitance, in uF
You can augment the ripple rejection at the source by placing a 470uF capacitor right at the output of the supply. This makes the high frequency return path as short as possible. This would reduce the ripple down to 19 mV in theory, but still that ESR thing -- likely you can get 470uF capacitor with 0.05 ohms ESR, so now you're down to around 50 mV at the PS output.
Now, how much rejection do you get from the choke?
The datasheet has an attenuation chart.
Not much around the 100 kHz range, but this is ok because capacitors do this work for you. The choke will take off those high frequency spikes that manage to couple into everything and get demodulated into audible noise. My conclusion is the choke you selected will be a good match for filtering switching power supply noise (probably overkill).
Capacitors after the filter can just mirror the capacitors on the input side. In other words do this:
470 uF -> choke -> 470 uF
And you will have a reasonably clean supply.
Another (cheap & dirty) thing you can do is to add a 0.1 ohm resistor (>1/2Watt) in series with the supply output (ahead of first filter capacitors). This wastes some power but it somewhat damps the resonant network between the L's and C's and adds some series impedance to knock off ripple against capacitor ESR. In other words, the "cheap & dirty" looks like this:
0.1R --> 2x470uF
And that just might be enough and then you don't need an expensive choke.
The main advantage of the choke is it takes off the high frequency spikes & ringing which (as mentioned above) seem to find their way into everything and get demodulated into audible noise.
Here is a good experimental sequence to follow:
1) Add 2x470uF capacitors to the output.
Noise ok?, done, Still noise? #2
2) Add the 0.1 ohm in series with PS output to work against the capacitors.
Noise ok?, done, Still noise? #3
3) Get rid of the 0.1 ohm and use the bridge of 470uF capacitors and the choke.
Noise ok?, done, Still noise? #4
4) Add the 0.1 ohm back in so you have the 0.1 ohm, 470uF cap, choke, 470uF cap.
Noise ok?, done,Still noise? #5
5) Start looking further downstream for where noise is getting into your system. Try the audio pass-through example so that you aren't using analog inputs for anything. Then add a volume control where audio is multiplied by reading off a pot coming from analog inputs.
Here is one way of filtering pots on analog inputs. Keep in mind the resistor divider between R6 and combination of parallel pots aims for 4.096V assuming 5V input. C1 takes off the incoming noise so the pots see a stable reference.
You could also use 3.3V (which will be cleaner) and connect the junction of R6 and C1 to the REF pin on Bela ADC.