There are two issues implied which are separate questions, requiring separate answers.
1. What time should a bochur daven bein hazmanim? As was answered eariler in this post – before the end of zman tefilah.
2. How should a bochur budget his time during bein hazmanim? Long answers needed, and will vary greatly among bochurim. There should always be learning time. Some helping around at home. Some leisure time. The formula (I may have omitted some things) is unlikely to be identical between any two bochurim. But there does need to be responsibility. Humans are not driven by instinct, but rather by saichel.