newbie!
It sounds like you are doing great!
During that get to know phase, my bf and I took walks, played Frisbee and basketball, hung out and shared our music tastes, and met for coffee after classes. We just kept things short, and low-key and talked a lot face-to-face.
It was about 2 weeks after hanging out that he asked me to a school dinner/banquet he had. After that we both planned our next date together and split the cost.
Miniature golf was a fun date because it was early afternoon and outside, we went for pizza after and then to a different place for ice cream. It kind of keeps things moving to have different places to go. IDK, do things where you will be comfortable.
I tend to like dates where you can do something, talk and learn about each other. (Game type dates help me learn how a person wins, loses, and basically his sportsmanship. Also, if he knows how to have fun or makes everything a competition.)
There's no time frame, go with your instinct. I think the zoo was a great idea for a first meeting; always go for that public place with lots of people around you. So, well done!
Best wishes!