Executive Summary Conclusion:
Michael's analysis is correct. The image diameter in the focal plane is
TH*f, where TH is the angle subtended by the sun (.0095 radians) and f is
the lens' focal length.
The important quantity (to maximize for igniting the paper) is the energy
collected per unit image area.
The energy collected goes as D^2 , where D is the lens' diameter. This
energy is spread over an image area which goes as (TH*f)^2.
Thus the energy collected per unit image area goes as (D^2)/ (TH*f)^2. This
is equal to 1/(F# * TH)^2, where F# = f/D is the fstop value of the lens.
Since we, confined to Earth, have no control over the value of TH, the
quantity to minimize is the fstop value = F# = f/D.
Choose whatever you would like to include among "all things being equal".