Moving Into Strength Training Phase - Need Efficient Ideas

Hello My Fitness Friends,

It's been quite a ride since last Thanksgiving when I got the flu (ironically after getting a flu shot) and couldn't eat for 3 days and lost 10 pounds. That kicked off a whole new wave of motivation to keep going and lose weight and then get back into shape!

I've lost 35 pounds and now I am NordicTrack-ing my way back to fitness. My wife has already remarked that she sees muscles on me that she hasn't seen for over 10 years!

So I want to take it to the next level and really add some strength training. My major challenge is finding the time. Or more accurately, making the time I have for exercise more efficient.

I've been doing a lot of reading and here's what I've come up with for a possible exercise program that might get me some results. It will always include the NordicTrack for my cardio workout.

3 days a week 30 minutes NordicTrack cardio at high resistance and 20 minutes for abs.
2 - 3 days a week 20 minutes NordicTrack cardio at low resistance and 30 minutes for upper and lower body.

So here's the question I have for this forum. What exercises can I do in the time alloted that would cover the 3 main muscle groups without having to resort to weights?

I figure I'll definitely be doing push-ups and pull-ups (need to install a pull-up bar somewhere), and I think as someone suggested here that 'mountain climbers' might be great for the legs. Aside from crunches, are there better ab exercises that I don't have to do a million of that will work upper and lower abs and the obliques?

When I was in my 30s I had like 3 hours a day to workout, so I got an entire gym full of weights and lifted like crazy. I did get in the best shape of my life. But now in my mid-forties, with a full-time job and a family to take care of, I need to get useful results while only having 50+ minutes 5 maybe 6 days a week.

There's gotta be a nice efficient program of calisthenics out there that I can adopt. And Ideas?

Cheers,
Nick