The Due has a digital-to-analog converter on board. If you use that, instead of pulse-width modulation, you'll get much better sound without the necessity of a sharp cutoff filter. In that sense, the Due does some of the things you need, "automagically."
Here's a tutorial describing how to drive a speaker from a Due DAC output: http://arduino.cc/en/Tutorial/SimpleAudioPlayer. But don't hook it up just yet. Note that the tutorial has this line:
For a simple test you can attach a pair of headphones directly to ground and DAC0
I'd recommend that you don't do that. The Due's DAC outputs seem to be fragile, and headphones are generally "poorly characterized" when it comes to impedance. Also, the maximum allowable load current for the DACs isn't specified in the SAM3X/A datasheet. The SAM3S datasheet describes the minimum load resistance as 5,000 ohms, as discussed here: Do not follow Simple Audio Player example - DAC0 now non-functional on DUE - #20 by stimmer - Arduino Due - Arduino Forum. That's a lot higher than a typical set of headphones. So, I recommend against testing the DACs by directly connecting a set of headphones. Other posts in that thread describes the mysterious failure of a DAC0 output, suggesting that the output is a bit finicky.
Note, too, that the Due's DAC output ranges from a low of about 0.55V to a high of about 2.75V. That won't affect operation with the DAC output AC-coupled. A lot of people have been surprised by it, though.