If you're training solidly, you'll start seeing results within a few weeks. In the army in my late 20s I went from totally unfit to doing 100 situps, 20 pushups and running 5km in 12 weeks. That was intense though.
I do a lot of modified exercise at the moment, pushups on bent knees or against a bench, that kind of thing.
As for a shapely butt, I dunno - get into those squats!!