Selecting the keys in your vi 'vocabulary' is a very personal thing. I have categorized the keys into several separate functional groups. As I get more time, I will try to organize these groups so that the first one or two keys in each group will be all you need to get started.
Most important in vi is to remember that there are several distinctly different modes. ESCAPE always brings you back to command mode, from which most of these keys can be typed. You can be sure you are in command mode by hitting escape, even if you are already in command mode.
Also, there are several groups of keys that do similar things. For example, there is a set of keys that puts you into other modes from command mode. (It is a good habit to get use to hitting escape after you are finished with a particular mode so that vi is in the command state when you finish that change.)