After breaking backlog items down to sprints, how should we partition the sprint items among the team ?
Work towards a self-organizing and cross-functional team
Looks like your first question is how to carve out sprints from the product backlog. The Scrum team should work towards delivering a potentially releasable Increment of “Done” product at the end of each Sprint. You may or may not actually deploy at the end of each sprint.
In order to accomplish this, the Product Owner should go through the backlog items and prioritize the features. The Product Owner should also articulate a goal for each sprint. During Sprint Planning, the team works with the Product Owner to carve out the Sprint Backlog. This is the set of stories that represent the higher value features.
Looks like your second question is how do I assign stories from the Sprint Backlog to individual developers. Scrum teams should be self-organizing. After the Sprint Planning meeting, team members should take up stories in the priority order and assign tasks among themselves based on not only their skill but also whatever needs to get done in order to create the releasable product. Try to break out of skill silos (such as developer, tester, designer) and aim for cross-functional capabilities.