Rear sway bar. Use the 06-11 rear Si sway brackets and go with either the 2014-2015 Civic Si rear sway bar (20mm) or the 2006-2011 Civic Si sway bar (17mm). I personally have the OEM 20mm bar on the rear and I really like it. I don't recommend upgrading the front bar as you will introduce understeer. You can replace the soft old rubber sway bushings and go with a higher durometer bushing like MOOG, ACDelco, or something else thats aftermarket.
Edit: if you want to use the 9th gen rear bar I would recommend using the 14-15 civic Si brackets instead of the 8th gen brackets because they are reinforced for the bigger bar. I didn't go this route and used the 8th gen Si brackets instead but your choice to decide.