In terms of what should be avoided, I think it has to do more with maximal exertion force than it has to do with the specific movement. I've been doing a fairly tough mma-style workout (google Bas Rutten's all around workout for more info), 30 minutes of pushups, bodyweight squats, shadowboxing, sprawls, etc. etc. I do substitute hamstring exercises for the ab exercises.
No discomfort in my stomach, and I started doing this I think about 9-10 weeks out. It is a strenous workout, I often can not continue doing push ups or squats from the burn/fatigue. But it's probably different on the body than trying to lift very heavy weight. You can get in very good shape without actually using weights, just using bodyweight, so it's not necessary to move lots of weight to have a strong/attractive body.