How to create a report to visualize different types of task by user

I'd do a task report (or an assignment report if you're wanting to pull task and issues) grouped by assigned to. You can have 2 filter sets in the report: 
Assignment users name = (all names of those you want to pull, or you assignment users home team, group, etc.)
Task status = statuses you want to pull
Add an OR filter set below it with:
Assignment users name = blank (or teams, etc. You put blank in order to get tasks that are unassigned).
Task status = statuses you want to pull

I say assignment users not assigned to bc assigned to will only pull the primary assignee, so you'll miss out on tasks assigned to multiple users by only using assigned to.