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Not as bad as people make them out to be, I think they are actually kind of fun. (Then again I am also the girl who runs half-marathons "for fun" so take that as you will.) But I hate the name. "Burpee?" Ugliest name for an exercise ever.
As far as strength training goes, there's pretty much no reason not to do it. Or rather no good reason. Here's an article on a beginning body weight workout and a video demonstrating moves as well:
http://www.nerdfitness.com/blog/2009/12/09/beginner-body-weight-workout-burn-fat-build-muscle/
Even if they're talking about weight lifting, I do NOT agree with waiting on that and concentrating on cardio. Because when you strength train - via lifting weights or just body weight exercises - you build muscle, which helps your body burn fat even in a resting state. The advice to not do strength training and focus on cardio is rotten advice and you should ignore it. You absolutely need to do strength training.