Would one choose an op-amp first, then important the SPICE model, then finally play around with the feedback capacitor values? What type of current source would you hook up to the op-amp and what analysis method would you use? I am only really familiar with basic DC steady state analysis in LTspice. However, I am keen to learn.
As I recall, there are generally two fundamental bandwidth limiters of a traditional transimpedance amplifier -- which one dominates depends on the circuit properties.
1. Single-pole response of feedback resistance and parallel capacitor: for high-gain applications in particular, this often limits amplifier bandwidth. Since it's a single pole response, it tends to be a smooth roll-off.
2. Double-pole response of input capacitance and effective input inductance of amplifier. This moves based on amplifier bandwidth product.
You might wonder where the "effective inductance" comes from -- afterall, there is no inductor in your circuit. It comes from the input impedance of the amplifier (i.e., impedance seen looking "into" the inverting input pin). The impedance looking into that pin will be near zero for frequencies in the closed loop bandwidth of the amplifier, but it will start increasing with frequency as your amplifier runs out of gain. So, in the frequency domain, this looks like an R-L network.
Lots of good resources about this online. Photodiode amplifiers by Jerald Graeme is an old book now but it explains this pretty well as I recall.