Microprocessor Generation of Summed Sine Waves with Random LF Modulation

I would like to program a micro to do the following:

1. Generate five audio frequency sine waves at different frequencies and amplitudes
2. Sum the above sine waves into one signal
3. Generate a pseudo-random low frequency waveform at a set amplitude
4. Multiply the two signals above so that the summation of the five signals randomly changes in amplitude and frequency.

What would be the recommended approach to this in terms of chosen micro (prefer PIC if possible) and design of the code? I am asking for general advice on how to get started with this project.