I often can't find my sent mail in my Gmail account viewed on my Mac in Apple Mail. I did not set up these folders, but I have both a "Sent Mail" folder indented under a "Gmail" folder and a "Sent Messages (gmail [accountname])" folder in my Gmail account in Apple Mail. Sometimes a sent messages shows up in neither of those, but I can find it by searching for it.
Some incoming messages do not appear in my Inbox, but are in a box I did not set up labeled "Important."
How do I set the Gmail settings and filters to avoid these two problems?