the better part of (something)
The majority of something. I'm sorry I'm late—my doctor's appointment took the better part of an hour.
best part of something
almost all of something; a large part of something; the major part of something. The discussion took the best part of an hour. The best part of the meeting was taken up by budgetary matters.
the better/best part of something
most of something: I worked at the camp for the better part of the summer.He had lived there for the best part of fifty years.