What type of schematic to use for a symmetric power supply?
LDO's have low output impedance but if the pulsed current exceeds the regulator rating, then additional storage capacitance is needed where C=I*dt/dV.

Generally high power audio systems do not use cheap simple LDO's but for low power , your approach is good.  Bipolar supplies allow direct coupling down to DC if you want.

Generally I choose input storage cap and load R such that RC = 8/f for 10% max ripple voltage (Rule of Thumb) at input frequency , f.   

Thus for you f=100Hz , if say load worst case is R=1k , \$C=\frac{8}{f*R}\$ = 80 uF (microfarad) and you have 1mF=1000uF so this is overkill.  You could use 220uF for good results and anticipate &lt;5% input ripple. 

Beware that LDO's have a 2V drop depending on load current. (check specs)  And bridge rectifiers raise no load voltage by 1.414 minus 2 diode drops and +10% allowance for transformer voltage with no load

There are other ways to calculate this using \$C=I * \frac{dt}{dV}\$ with \$I=\frac{V_{{in}_{min}}}{R}\$ so \$C = \frac{Vmax * dt}{R * dV}\$  so you choose you Vmax , dV for duration of a about 1/3 of a cycle of your lowest bass frequency without loss of voltage regulation.


  I now see the 5W or 5VA transformer rating so max power is 5VA/(12+12)V= 200mA best case and V/I=R=12V/0.2A=60 Ohms if want to plan for future loads so your input voltage will start 50% higher than 12V and drop with load depending on ripple voltage. ( I wont bore you with calculations)


Misc info



All dielectrics have this equivalent circuit which results in a self resonant frequency where Zc(f) is lowest.   By shunting caps of smaller values extends this low impedance at higher frequency for the range required.   

For e-caps or electrolytics which have highest density ( yet only 0.1% of a battery F/volume) but much higher ceramics they tend to have a much lower SRF but much higher C. A useful thing to rememmber is the quality of any electrolytic may be judged by its ripple current rating and better by it's ESR.  For any family of caps and brand you will find in certain voltage range that ESR*C=T is constant.  For the best e-caps used in SMPS, these are as low as 1us and the best microwave ceramics this will be &lt;&lt;1ns but for audio you don't need this bandwidth but you do want the drivers to have very low source impedance which is in series with your power regulators and input Caps. So for source impedance of 1% of load or an Audio woofer dampening factor of 100x on a 8 Ohm load you want Caps with an ESR &lt; 80 mΩ and possibly lower so watch out for this value.

Now if the very best e-cap is T=1us and the cheapest GP cap is T=200us  , which do you get?  You need large supply high bass current with low ripple and you need small ceramic or plastic caps for high frequency pulses since they have more bandwidth, but since Zc(f) drops with rising f, you will often see 1000uF//10uF//1nF or variations of this depending on your power. For 100W you might see 100mF//100uF//1uF//0.01uF but it depends on the ESR and cost of each component and quality of the audio system design.

Now you will find General Purpose e-caps (Cheap) will have ESR*C = T = 200 us or in milliseconds in massive size and many seconds in batteries.  We also know BW=0.35/T for rise time so a cheap cap has less effective Bandwidth.

You will find a lot of other resources on the net and in this forum about the unique characteristics of every dielectric material, that tradeoff density, ESR, temp stability, cost, size, voltage rating, polar or non-polar etc.  Non-Polar e-caps are fundamentally two polar caps in series (+- -+) that may have reverse diode protection.