I personally maintain separate pages for each “category”, for example one for work TODOs, one for personal etc.
I make use of due dates heavily to surface things in my home/index page. I have 2 main queries in my index page, one to show me TODOs that I marked for today, one for ones that I missed(due before today).
I also have other queries like, tasks coming up for the weekend, or tasks I completed yesterday(mostly for work standup meetings) and task completed in last week. You can find out about the queries I have in my index page here.
As for clearing completed TODOs from the page, I like to retain a history of the things I have done and so I have an external script that I use to move the items into a separate file. It refiles the completed items into separate files under year/month folders. You can find the script here.