Common Filter Types for Audio Applications
a lowpass with variable cutoff frequency and resonance.


RBJ has a cookbook on how to do this:

http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt

Here the cutoff frequency is called w0, and the resonance is called Q:

LPF:        H(s) = 1 / (s^2 + s/Q + 1)

            b0 =  (1 - cos(w0))/2
            b1 =   1 - cos(w0)
            b2 =  (1 - cos(w0))/2
            a0 =   1 + alpha
            a1 =  -2*cos(w0)
            a2 =   1 - alpha


If you want to vary these parameters continuously while passing signal, you are not supposed to use biquads (because updating the coefficients causes glitches?) and you should use state-variable filters instead:

http://www.earlevel.com/main/2003/03/02/the-digital-state-variable-filter/

This is also a 2nd-order lowpass with variable Q.


  Does anyone have insight into filter types commonly used to mimic the sound of traditional analog gear?


Generally any filter transformed to a digital IIR using the bilinear transform is an "analog-like" filter.  Bessel is an exception because the important property of a Bessel filter is its group delay, which is not preserved by the bilinear transform.  Bilinear transform attempts to preserve the frequency response primarily.