Mainly impedance and matching, then noise figure, and bandwidth. But it depends, and any one of these may take priority. A tuned RF amp for example might not need much bandwidth (and can make up any impedance high or low with matching networks), but a wideband amp has no choice but to use low impedances; and noise figure curves tend to favor surprisingly low currents, which can make wideband low noise designs problematic.
An active nonlinear / bilinear block like a mixer, will see these vary with operating condition, and during a cycle, so the nonlinearities must be managed for the application. The input nodes can have fixed (source) impedance, and the collectors can have fixed (load) impedance, but the middle (C to E) node(s) have impedance inversely proportional to instantaneous current (r_e ~ Vth / Ie) which ultimately limits bandwidth. Additionally, the noise factor at the inputs and outputs will matter, if that's a concern.
Tim