What factors should I consider when choosing an IIR filter realization?
First of all, a bit from wikipedia on Direct Form I and II implementation. 

Direct form I requires more memory, but is a somewhat simpler strategy, and is less likely to have round-off and resonance problems.

Direct form II requires less memory, but it has the potential for unusual interactions, larger numbers, and more round off error. Much of this can be reduced by cascading smaller filters, especially 2nd order filters.