I would always recommend trying the TSL257 and similar - these have photodiode and op amp in one neat little package. Get them in IR or visible. Save a lot of trouble with just three pins - gnd, supply, voltage out. Almost bomb-proof and work with output close to supply. Just needs a bypass capacitor and a small load resistor
Not too sure what you want the second op amp for - buffer? unity gain? inverted output? It should be straightforward to add a second amp to do any of those functions
Are you getting anything sensible from your first op amp?