Good job on getting back into lifting!
I would, if you haven't lifted in a few years, start with more total body training. Either that or a upper/lower split. Im bias towards that because thats how I lift. I suggest the main compound lifts. Squats, deadlifts, presses, lunges, push ups, core work.
It'll kickstart your metabolism more, recruit more muscle fibers, and make your workouts shorter (and tougher).
Watch the diet, and incorporate some cardio and you'll see what you want --"gain strength and some lean size"
I do think splits (like the one you listed) can make you stronger but only if youre an advanced lifter (interested more in size gains and looks) who wants to really hit certain muscle groups.