weight training advice for novice

So, I'm an older guy (53 years old) and decided I wanted to start strength training about a month ago after not having done any resistance training since I had rotator cuff surgery in 2015. My goal was to lose a little weight and get my body composition back to where it was a few years ago.

I'm 5'9" and weigh in at 157 lbs down from 170 lbs. on Oct 31 (happy at that weight and could live a few pounds on either side of that). I went to one of the nutrition stores because I wanted a quick estimate of body composition and measured at 13.9% body fat. Can't recall all the other numbers off the top of my head, but you probably get the picture from that.

I won't go too much into my diet, except to say that I log calories (meticulously), and am slightly hypocaloric with a goal to get to .8-1 gm protein per pound of body weight per day (I have a hard time getting there and staying within my calorie budget and usually am around .65 gm/lb).

Here is what I do for resistance training:

"A" day: Mostly chest, shoulders and core - lat bar, bar bench press, dumbbell bench press, dumbbell military press, dips, converging shoulder press, seated chest press, flys (those three are machines), captain's chair leg raises, incline sit ups and Roman Chair back extensions.

"B" day: Mostly lower body, arms, and core - Squats on smith machine, leg press, barbell curls, dumb bell curls, triceps cable pulldowns, face pulls, and shoulder shrugs with the same core workout noted above.

I get my cardio from stairs (usually around 100 flights a day in my building) and tennis a couple of times a week. Gym is 4-6 times a week.

I would appreciate suggestions on modifying or streamlining what I'm doing for most efficient gains, I'm pretty well maxed out on the amount of time I want to spend relative to work/life/family balance - not looking to bulk, just get stronger and stay lean. I would like to avoid a trainer so as to maintain my time flexibility.