Good practices for full-custom IC measurement?
I would start by checking app notes for similar parts on Analog, TI or Linear (also analog now) websites. There are app notes for characterizing any part of an op amp, including testing bias current, open loop gain, noise and more.

With all of the information on manufacturers websites, there is enough information to learn how to design, build and test most of the circuits that they make. All you need is a lot of reading time. 

Edit:
Here is a collection of circuits (or actually just one circuit) to test for Offset, bias current, DC gain, AC gain, DC CMRR, DC PSRR, AC CMRR and AC PSRR. 

It would do well for you to start poking through manufacturers websites and start reading app notes, get familiar with Jim Williams and Bob Pease