Transimpedence amplifier output from 0 to 3V
I would like the output to vary from 0 to 3V.



You could use a resistor potential divider at the output to reduce 5 volts to 3 volts.
If your circuit has too much sensitivity then lowering the 1 Mohm to 100 kohm reduces sensitivity by 10 for instance. This might be a possible alternative solution



  I am also unsure what values of resistor and capacitance to pick.


The feedback resistor value sets the photo-gain of the circuit. If the photodiode produces (say) 1 uA for a given incident light power then the op-amp output will convert that to 1 volt when using a 1 Mohm resistor and 0.1 volts for a 100 kohm resistor.

The capacitor is used to reduce noise and is based on the capacitance of the photodiode. The bigger the PD capacitance, the greater the feedback capacitor needs to be to achieve the same noise levels. It's related to a thing called noise gain.