I spent a few months last year recovering from a shoulder and arm injury that was exacerbated by poor overall strength (I just turned 50 and, though I am pretty active, I hadn't worked out with weights since my early 20s). My physical therapist was frank with me and said that if I didn't start working on my overall body strength in a real way, it was going to be downhill from here in terms of joint problems and injuries.
I took it to heart and started to try to develop a weight training schedule but was quickly overwhelmed by the amount of time it seemed like I'd have to put in (leg days, arm days, chests days, etc.). I finally found a trainer whose philosophy is that all you need is two 25-30 min., high intensity workout per week, hitting all the muscle groups each time. The high intensity (i.e., limited to no rest between sets) aspect makes it as much a cardio workout as a weight workout. It's been a revelation. I've lost 15 pounds in five months (while adding muscle) and at age 50 am now stronger than I was at 25.
My takeaway point is, if you can find a half hour twice a week (while also paying attention to your diet -- getting more protein, fewer carbs, and as little sugar as you can manage), you can really get good results.