OPA350 for single supply applications and it also has low input bias current (pA range).

Thanks for this tip! This could be right on the money.
What I like about OPA350 is that it can operate of a single supply "as low as 2.5V". Small MSOP package is good too.

 

Thanks I'm researching the opamps for this circuit. I have only one desirement about the opamp: it would be nice if it could operate of a single supply rail. I've looked at the datasheet of the one that Ron have used. It's output can swing only between V(-)+1.5V and V(+)-1.5V. Ron's opamp has a JFET input stage, but the following stages and the output stage are BJT. Were BJTs chosen over FETs, because they generate less noise?

I have found a couple of other opamps:
TL082 looks very similar to Ron's LT1464
LT1013 single supply operation possible (p.8 of the datasheet)

I already rejected TL082 because it has too much input offset voltage.
LT1013 input bias current is 10 times the current you are trying to sense.
Keep in mind that, if you want the input summing node to be at zero volts, the output of the op amp will have to swing negative. A single supply op amp won't do that unless you use one with supply pins connected to zero and -V, and then your input common mode range would have to include the positive rail, which you can get, but as it stands now, you have a positive supply anyway, so you might as well use two supplies. Did that make any sense to anyone besides me?
If you REALLY have to make it work with a single supply, we might be able to create a midpoint reference and take off from there. Why don't you see if this scheme works first? There are too many unknowns for me to take off on another design, when we don't even know if the general idea will work.
BTW, the second op amp is the other half of the LT1464. As such, it also has JFET inputs. The bipolar output stage is just there to get well-defined logic levels.

 

[...] Ron's opamp has a JFET input stage, but the following stages and the output stage are BJT. Were BJTs chosen over FETs, because they generate less noise?

[...] The bipolar output stage is just there to get well-defined logic levels.

May be we are not on the same page here. I meant the stages inside the OpAmp. It's just a matter of curiosity, though.

 

I think, I have figured out how to make the transimpedance aplifier work with a single supply. It simulates with the LTspice quite well (DC only, though; haven't tried AC and transient yet) and should fit well with the rest of the system. Now I can filnally submit the "paper design" and move on to breadboarding.