It sounds like the StellarEquilibrium has easy access to "The Rest of the Robots."
Simply put, it is not catastrophic to read "The Rest of the Robots" before "I, Robot." I think the question is whether you should or not, and in my opinion there is no reason not to read "I, Robot" first. You should be able to get a copy at just about any library, or a simple web search. If anything, you should have an understanding of the Three Laws of Robotics before moving on to "Rest of the Robots" however you might glean the nuances just from the stories as you go along. If you really do want to read "The Rest of the Robots" first, just read the Wikipedia entry and stop before you get to History as there are some spoilers for some stories and novels.
What would be catastrophic would be to have the "I, Robot" movie be your primer on the Three Laws of Robotics. If anything, skip that and go right into "The Rest of the Robots".