I often find it to be a challenge to make a rental space feel like your own. You can't make any permanent changes, and you don't want to invest too much in the space when you don't own it! I ran into this challenge while setting up my closet when we moved into our new (rental) condo. The closet was originally just the one bar across with a shelf on top (I should have taken a before shot!) and I needed to find a non-permanent way to add more storage space. I found this Extend-It Closet System at Canadian Tire, and it was the perfect solution! You can customize the bars however you want and it's portable for when you move.
My other organization solution was for my bags on the top shelf. I often find they end up in a huge pile, but with these book-ends from Ikea they stand up neatly and it's much easier to see them. (I found this idea on The Glamourai) The hooks on the closet doors and the basket for my chunkier scarves all also aid in keeping my things tidy and accessible.
Note: I swear my shoes aren't that dirty, it's just how they photographed!