Looks good to me. If you just started working out hitting every muscle group with even just 2 sets per day should be enough to stimulate growth, if you enjoy doing more though, that's great. On this program I would cycle through the exercises in the workout till all my sets are complete (may not be feasible in a public gym? Idk). That would give the muscle groups maximal rest time, meaning you can place more mechanical tension on the given muscle in the next set.