When I met my first sponsor our first meeting consisted of me telling him my story. In our second meeting he told me his story. We started on step 1 in our 3rd meeting. It's hard to say what your sponsor will do as there is no one right way to sponsor someone, but hopefully he won't wait long to start the process of having you reading the literature as a starting point. When we started on the steps my sponsor would have me read a certain part of the BB and/or 12&12 and then we would meet to discuss it. When he felt like I had a full understanding of the corresponding step we were discussing we would move on to the next step.
As for what to look out for this is only my opinion, as I stated there is no one right way to sponsor someone. I ended up leaving my first sponsor when it seemed we were getting bogged down with the minutia of each step and the corresponding literature. Everyone coming into AA has different circumstances when they arrive, and for me personally I was in desperate straits and needed relief. I found another sponsor who took me through the steps using the BB in about a month. Again that is what worked best for me so that's what I looked for. My first sponsor is a great guy and we are still friends today. He just had his own style and at the time I felt I needed someone else. I wouldn't hesitate to ask him to take me through the steps in the future now that I am on solid footing and could probably benefit from a more in-depth process.