Circuit design using 2-stage opamp
It is best to increase gain at the TIA because it improves SNR whereas increasing gain at the voltage amplifier mostly just changes the signal level. You will need to decrease the feedback capacitance to maintain the same bandwidth. Your maximum possible bandwidth will decrease since you are increasing the high frequency noise gain (1 + Cd/Cf). Increase the feedback resistance and decrease the feedback capacitance as much as possible while achieving your target bandwidth, then increase the gain of the voltage amplifier if needed.

To minimize DC offsets and read 0V in dark conditions:

1.) Match the impedance of the inverting and non-inverting inputs of the TIA. Choose an op amp with low input offset current. If you are using very large feedback resistors, be careful that the (input bias current) * (feedback resistance) is within the common mode input range of the op amp.

2.) Choose op amps with low offset voltages: the TIA is less sensitive to offset voltage because Vos will experience a gain of ~1 if your photodiode has a large shunt resistance. Vos matters more on the voltage amplifier, especially if it has significant gain.