Finding the right MOSFET for project
A MOSFET will be a good choice.
The following gives a guide to directions - ask more questions. 

Load max sounds like (pun notice retrospectively) LED strips at 12v, 10A
MOSFET needs to switch this load so 20V+ rating desired, usefully more than 10A - say 20A+.

Now the fun begins.
If the FET is hard on then dissipation is low. With and Rdson (= on resistance) of say 10 milliOhm the power loss at 10A due to channel resistance = I^2R = 10^2 x 0.01 = 1 Watt.
If you PWM switch the FET you add switching losses but losses are still "moderate"
If you linearly switch the FET so it acts like a resistor dissipation is much higher.
A 12V LED strip will decrease to close to 0% current by 8V (or higher) probably, so if full load is 10A you will probably be down to 5A at 10V (so driver loss = (12-10) * 5 = 10 Watts, and down to say 1A at 8V (loss = (12-8)*1 = 4 Watts.
So you can probably expect losses in linear mode to be under say 10W but allowing for 20W may be safe. Rdson becomes non-critical when used this way as resistive on losses swamp Rdson. 

So, we have a MOSFET rated at ~~~= SOME OF 20V, >10A and 20W actual dissipation and Rdson = 10 milliOhm.
I say "some of" as you don't need Rdson low in linear mode but you don't need as hogh dissipation in PWM mode.
For 1 off amateur use specify leaded TO220 package for easier use and ease of heatsinking.

Searching DIGIKEY with
MOSFET 30V 20A TO220
then sorting by ascending price and looking for lowest $ in stock 1 quantity parts gives as below. I didn't specify Rdson but could have. 

Infineon PSMN022-30PL - datasheet here in stock at 73 cents US in 1's.    Pricing
30V, 30A, TO220, Rdson 34 milliOhm max at 5V gate drive, 41 W max dissipation, 

See fig 1 for max dissipation based on heatsink temperature.
Thermal resistance is 3.6 C/W junction to case so you'd want to keep dissipation under 20W and ideally under 10W - SO probably OK.

So - how do you drive this.


You MAY be able to drive it straight from the amp with a potentiometer to adjust level.  MOSFET in linear mode, probably. 
Feed amp output to a comparator to make rail-rail signal and drive FET. Lower dissipation. Don't exceed max gate drive. May not look like what you want to see. May. MOSFET in PWM mode - low losses. 
Use a linear amplifier to adjust level up or down as required. Can add simple filtering to adjust hang time, attack time, frequency response, more ... . These are all "easy enough" but lets see if this is what you want. MOSFET in linear mode.




... 30PL - slightly better Rdson, slightly more $

Wow!
Infineon IPP065N03LGIN - pricing and datasheet
30V, 50A, 6.5 milliOhm Rdson, 2.7 C/W,   TO220 
10 milliOhm Rdson worst case at gate drive of 4.5V.
$US1.05/1 in stock.
Looks very good for this task.