You can get further than you think with VERY basic exercises.
The issue I see
mid to long term with doing a randomized EOTD and Daily Workout is that these will not help you track your own evolution. Still better than nothing!
My opinion, and how I would do it, starting from a sedentary level (because I am right there too! starting over, 3 weeks in at the moment):
Do
Foundation Level I (30 day entry level program). I absolutely love that routine for moving everything every week a little, and get out of basic soreness. I do it before work as well. Like before 6:30AM.
My personal plan, after Foundation, is to do the
Push Pull Legs program. It has weights. The weights can be increased over time to keep reps in the low numbers. My idea is to branch off of that program and start my own routine that will keep pushing me to failure in a short number of reps (8 max).
With limited time, what you may want to look for is something that never increases a lot in reps, but keeps challenging you - so an increase in difficulty once you reach a level.
In fact, if you give it your all in a short burst of time (i.e. to failure), this will guarantee the best evolution in your personal goals. It will also likely challenge your energy levels and increase them over time as well. You learn to reach discomfort and push through a little.