Do the available repeatable quests,arenas and or events then for corresponding or desired hunt.
Investigations are not something that is going to be trackable due to how incredibly random they are and the variables vary to a point that pretty much makes each hunt unique and there for not really available to others to compete against.
Not sure what you mean by expanding? If a quest is not listed you can submit it under Not-Listed quest and it will be added once the moderators have had the chance to look at the submission. There is no equipment restrictions so i'm not sure what made you think there was any to begin with, just don't expect to compete with the fastest times overall unless your aiming for specific weapons. Weapons are tracked as a filter and not anything more.