Hello Christopher,
If you set the task so that the start and end date are today, then set it to recurr "Daily" and choose "Every 1 day(s)", then checking it off will change the start and end dates to tomorrow. Since the start and end dates are both after today, the task won't be defined as "Active", so it won't appear on any of your lists which are filtered to show only active tasks. Is that the behaviour you're looking for?
Regenerating a new task "x" days after completed means that it will calculate the due date from the date that you check off a task. So if a task is set to regenerate in four days but the next time it's due is in two weeks, then checking it off early, today, will set the due date to four days from today. Does that make sense?
Stéphane