As all the recommendations above are applicable, I will just add that the keys in the bang for the buck department would be stiffer springs and bigger swaybars.
Beyond that, you can look at shocks, bushings, etc... but that all depends on how much you want to spend, how hard you want to corner and ride, and how much you want to fiddle with it. Oversimplifying it, but beyond getting the sway in check and to your liking, spending money on good tires and track time is usually a good way to go.
Based on what you said and the photos, I would recommend the following in this order to minimize cost and maximize benefit:
1. Upgrade Front Swaybar to the biggest you can find... 1 1/8 or bigger if possible.
2. Add Rear Swaybar... you didn't mention, so presumed you need one. Rear should be at least 3/4 inch, but bigger is OK as long as front is about 1/4 to 1/2 inch thicker than the rear. If you can afford adjustable front, but especially rear swaybars, spend the extra money if you really want to be able to tune to each track.
3. Upgrade Front Springs to 600# or higher, but beware of the street driving tradeoff in harshness going much above that with a small block.
4. Upgrade Rear Springs but be ready to remove some leafs as needed to get traction and control oversteer due to lack of weight transfer if the rear is 'too stiff' relative to the front. Upgrading the rear springs should definitely be done after the first three items, and be ready to put the ones you already had back in... softer springs and a decent swaybar and shocks is usually all the back needs.
5. Make sure the front springs are 1-3 inches lower than stock (as low as you want given tires, bump stops, and denture chatter
. Also use a lowering kit for the rear leafs (1-2 inch aluminum block kits are inexpensive and pretty easy to install with 2 jacks and 1 friend.
6. Adjust your Koni shocks to full stiff if possible, or upgrade your shocks if they are not the premium/adjustable model.
7. Replace worn rubber bushings with poly, Delrin, or aluminum, depending on how hardcore you want to get.
8. Relocate the battery to the right-rear corner of the car. Start planning on othe frontend weight saving mods like aluminum radiator and heads, etc.
9. Tell passengers they must place half their body mass outside the window to compensate... just kidding. Never sacrifice safety for a lousy few tenths off your lap time.
body roll 
