Normally the pilot flying the sector does both the take off and landing. There are some company restrictions (weather related) placed on the FOs, but they don't come into play often.
The captain generally decides who will do each sector based on a mixture of whim, what he has recently flown, and weather conditions.
Other factors that come into play...sometimes the company will request a particular sector for an FO for a route check, or for recency. I need to do a Cat II/III soon, so that will need to be planned (probably for LA, as Melbourne is mostly on 34 at the moment).