I am over 5'9" and ride the 53cm pista. I tend to ride a smaller frame, but I would say the 51cm or the 53cm is the right place for you to start.
I would recommend measuring your top tube on another bike that fits you and looking for the correct track frame based on that number. I recently found that after some minor adjustments to all my rides (track, road, and fixed/trainer) I ended up with the exact same "cockpit length on all three bikes. I knew the general top tube/stem combo length that I preferred based on a pro fit from a year ago, but the seat fore/aft, was adjusted based on little tweaks for comfort. All of the bikes were within a couple mm of each other.