For the simple purpose of 'staying fit' I will recommend lifting weights.
Cardio is great and would suggest tacking on if you have the extra 15m to do it, but as mentioned above a walk/jog is free and you can do it anywhere (so just buy some gym shoes and when you have 10m just go out and run around the block a few times)
There are ways in which you can build a lifting routine that gets your heart rate up and keeps it up for the whole time (so its also cardio) with the benefit of working all of your muscles. You can loose fat, build muscle, improve cardio, and look and feel better! Plus it helps maintain bone density and the muscles needed for balance and everyday tasks that begin to degrade as we age.
Take 1.5hours - Do a warm up walk/jog for 10-15min, then 45min of larger compound lifts, followed by some isolation lifts/supersets, and then some stretching and cool down! Then just go walk and run as much as you can during the week lol
I would suggest finding a fitness forum however, they would be more qualified in giving fitness advice/routines then we are i would think. Bodybuilding.com is a great resource once you learn to navigate it (don't let the name fool you, its 90% people who are just working out for fun and health reasons like yourself!)