I am working with a legacy software project that already uses events as a category of [insert umbrella word here]. In order to have clarity of naming variables and classes, it would be perfect if I could use another umbrella word other than event to describe all three types: training, event, competition.
How about activity, as in
Select the type of activity:, borrowing from this definition from m-w.com:
a form of organized, supervised, often extracurricular recreation The camp offers hiking, swimming, and other activities.