Shorter workouts, for the most part, can be ideal for most, even advanced men. Probably a good idea is to start with the larger muscle groups. That seems to be the general rule of thumb for those kinds of full body workouts and for good reason. More effort with heavier compound movements, when the body is fresh for a training session. Changing the exercises each workout may work for some, so feel free to experiment for yourself. But sticking to one set of exercises, every workout for that training cycle, sets a pattern of increased strength and size for those exercises. Giving a steady rate of improvement.
Might try this order of movements if you are still going to use your original exercises:
Squat
BB row
chin
BP
dips
Don't know how many sets or reps your doing but I might suggest three for the squat's and the other ones, just two sets each. Abbreviated systems (must be a dozen or more out there) are meant for compound exercises with fewer sets. Usually done two to three time a week. Good Luck.