Parallel resistor before voltage amplifier
You could do it like the first diagram. The input current generates a voltage across R1, which is buffered and amplified by the amplifier. Unfortunately, you run into a very nasty compromise if you want speed from this arrangement. The voltage on the input of the amplifier has to move, which means it has to charge Cstray. Cstray and R1 form a lowpass time constant on the response of the system. Choose a big R1 for lots of gain, or a small R1 for lots of bandwidth, but you sacrifice the other parameter.
Cstray is inescapable. Photodiodes tend to have a large self capacitance, even if you can reduce that of connectors and cabling, and the amplifier input.



simulate this circuit &ndash; Schematic created using CircuitLab
In the second diagram, the virtual ground connection of the second amplifier 'short circuits' Cstray to ground. The amplifier input node does not have to move. You can choose R2 for gain alone, the amplifier takes care of the bandwidth. Spend more on the amplifier, you get more bandwidth. This configuration is called a TransImpedance amplifier, as R2 defines the ratio of voltage out to current in.