I've been berated for leaving the gym after 25 minutes. It's not about getting it done fast or slow, it's about what your goal is. I was working out 1 muscle, and 25 minutes was more than enough. for 200 or 400 push ups or even just 20 pushups you can get some pretty good results. And yea I meant core, because using good form is huge and slowly can get you that strain (that's where you start sweating and shaking). In boxing I was taught to explode and I'm actually a pretty angry individual so it works for me. It'd be very hard to hurt yourself without weights. I was a dummy once with 45 lbs as a warm up but without weight I'd consider almost anything safe.
fun story: I used to DJ at a 6000 capacity auditorium and there was a soundboard kid who saw the hockey players doing vertical presses against the wall. He came in with a lacerated leg after attempting it in his bedroom.... you just have to own your body and not let it own you. Starting at 100 pushups is just a warm up for the big boys at the fire hall. So do them however TF pleases you as long as you're getting where you want.
I'm no spring chicken, so really just want to maintain a reasonable level of arm strength rather than build towards the big boys at the fire hall. I have to worry about aging joints and the ghosts of past injuries.
It'll be interesting to see where my maximum reps end up given where I started - but I don't plan to do this for too long. Plan to do at least 30 or 40 days and might drop to about 6 sets a week after that.
One of my biggest take-aways from kinesiology was that if you repeat the same exercise perfectly executed, you will not be able to put forth a stronger effort than your first attempt. I believe that same school of thought can be applied to age. Today you can do more than tomorrow and so forth. So spring chicken or on the butchers block remember you're only given what you have. That being said, KICK SOME OLD MAN ASS AND LOVE THE PAIN!
Balance? Are you talking about core strength again? I think I have enough (just) of that. I'm mostly just trying not to get injured... though you make it sound like a party (given sufficient levels of anger).
Edit: I do the first half of the set almost as fast as I can because it's boring.. go slower towards the end when there's some strain.