Hey,
Apologies if this is a repeat, but haven't read all the replies (naughty me!) - but here's my ha'penny.
If I were interfacing to a current-output device, an inverting op-amp configurtation acting as a current-to-votlage (i-v) converter would be a starting point. In this application, op amps with rail-to-rail output and low current noise would be a good start (the effective output impedance of your diode will be high-ohms, so low voltage noise of little interest here). for theses general kinds of applications, I'd suggest low offset and low drift, but looking at the data sheet of your diode, the temperature dependence alone would negate any such care, unless this is mitigated.
In terms of using the optical device you've specified for absolute measurements, I'd look elsewhere for devices which have things like temperature compensation built in, or your circuit will have to get quite complex (relatively speaking). That IR diode you're listing is good for things like IR remote receivers, where you only really care about differences, i.e. the AC, (and you would arrange you're encoding scheme to remove dependence on any kind of DC-accuracy) - of course, with enough ingenuity, you can (mostly) cancel all the temperature stuff and other non linearities, but if sensing absolute light level is your aim, look at more sophisticated light detection devices, where some clever guys from the semicon MFR have done a lot of the hard work for you, building in things like temperature compensation
maybe go for all digital interface, something like the TSL2561?
again, sorry if I misunderstood your aims, or for any repetitions
Best regards,
Nat