This is what I would suggest:
10 min warm up via one of the following...
-Brisk walk.
-Light jogging.
-Stationary cardio machine. (ie, bike, cross trainer, rowing machine, etc.)
-Anything that will slightly raise your heart rate and get the blood flowing to your muscles to prepare them for whats to come...
Then do a full body stretching routine. Make sure you stretch the lower back, the abs and obliques if you can. AND TAKE YOUR TIME.
Then do a light full body workout with body weight only with some concentration on abs, obliques and lower back. (ie, crunches, back hyper extensions, sit ups, rocky sit ups, the works.). Make sure to maintain proper form, if you don't exercise proper form your problems might get worse.
Basically, by simply exercising with proper form your posture will get better. Sit straight and keep the arch in your lower back natural, don't force it. After a while your shirt will get tighter near the lats and near the traps, your shoulders will move slightly back your chest will stick out a little and your posture will hold itself without any effort. Personaly, after doing back hyper extensions and deadlifts I always have the feeling of having an excessively well postured upper body, it's as if my body is forcing it into the proper position and I love that feeling.
The exercises I would recommend:
Pushups.
Crunches.
Side Planks.
Sit ups or leg raises, I prefer leg raises they are easier on the lower back and have the same effects.
Body weight squats or lunges.
Supermans.
Back hyper extensions.
Assisted pull ups.
Toe raises.
Then after a while of doing these I'd get into free weights.
Have fun
