Amplify Microvolts up to Volts
You can definitely do it with op amps. 
Some things worth investigating


A 'T' feedback network in the op amp
Be advised of the issues with that much gain in an op amp. 
You will need to account for things like


Dynamic range
Signal to noise ratio
Current/Noise voltage (i.e. you will probably want most of the gain in the first of several stages as the noise voltage will go up with the square of the gain instead of linearly in subsequent stages)
The bandwidth of the signal you are capturing 



This is do-able, but it will be work. I'd advise looking up Ron Mancini's "Op-amps for everyone", Any book by Gerald Graeme, and a fresh copy of LTSpice to do your analysis first before even breadboarding. 

Sounds like a fun project. Good luck!