Yes there is a great variety of configurations to try.
Some circuits are better at amplifying current, some better at amplifying voltage, some are more sensitive, some respond more quickly, some generate pulses, some duplicate the waveform in the lightbeam, etc.
Photodetectors don't all have the same characteristics. So there can be more than one circuit that will work with your photodetector.
It depends on what works best with your photodetector characteristics, and the strength of signal it is receiving, and the ambient light conditions.
Which conditioning circuit to use will also depend on what you want the output to be like, as based on the next stage in your circuitry.
It all adds up to having to experiment. Start with what's easy and see if it's sufficient.
With a laser beam hitting the photodiode there's a chance you will get a strong enough response that you'll need little or no amplification. However you don't normally connect the photodiode directly to the next stage.
Start with a resistor above or below the diode. Tap between them and see what voltage you get when a beam hits it as compared with no beam.
If you get the wrong polarity then turn the diode upside-down. Etc.
If you need amplification: Try the diode connected in series with a transistor bias (not the most typical configuration, but you're just experimenting). Put a potentiometer in series set to high resistance to start with so you don't ruin the transistor. See if the diode produces sufficient current to turn on the transistor.
Turn the diode around if necessary. Reduce with the potentiometer if necessary. Or add more bias from an additional resistor network if necessary. Etc.
Or you can set the diode to bias the transistor in the conventional common-emitter configuration, etc.
Or set the diode in the emitter leg of the transistor and use common-base configuration, etc.
All depending on what voltage and current you are getting from the diode, and depending on what you need going into your next state.