Be wary of anyone who is so adamant about something as trivial as exercise selection. When lifting for fat loss and muscle preservation, you really don’t need to fry yourself every time you go to the gym. You can if you want, but you’ve figured out by now that diet is what drives your scale weight down. Lifting just helps it along and helps your body prioritize burning fat and keeping muscle. Back squats are probably one of the better tools that are out there, but goblet squats can be used to great success as well.
@planetcybertron gave some great advice and she’s walked the walk too. There’s a gazillion programs you can use and a gazillion set and rep schemes. I like the Dan John way of thinking (he’s an author you can search on this site).
Make sure your lifting covers the following movements, which it looks like you’re already thinking about.
Upper body horizontal push (bench press, DB press, push-up)
Upper body horizontal pull (DB row, barbell row, fat-man pull-up)
Upper body vertical push (strict press with barbell, dumbbell press, kettlebell press)
Upper body vertical pull (pull ups or lat pulldowns, vary your grips)
Squat of some kind (high bar, low bar, safety bar, front squat, goblet squat or even just an air squat)
Hip hinge of some kind (deadlift from the floor, Romanian deadlift, stiff leg deadlift or even kettlebell swings)
Loaded carry (farmers walk, sandbag carry, db carry, trap bar carry, lug some rocks around in a backpack)
Hit those once per week and you’re stimulating every major and nearly every minor muscle in your body too. You’ve lifted. Good job. Then do some food prep or go for a walk.
You can do stuff like train your abs directly, train your biceps directly, do leg machines or any machines. Or not. I don’t think they are necessary when lifting for fat loss and muscle preservation when dropping weight. They are great if you’re trying to add weight and muscle to your frame, but that’s not the game you’re playing.
There are lots of great fat loss articles on this site, and not all of them will have the movements I listed and that’s fine too. Also, keep in mind that you’re not a bodybuilder losing fat to get into contest shape. You’re just a regular person dropping fat, which is good news for you. You don’t need to do what already lean bodybuilders do to get into contest shape. Make sure you’re picking a program relevant to your situation.
Search around and find one you believe in and can do in your workout space, then commit to it and go. What you already laid out is fine to get moving on as well. Maybe not optimal, but don’t let perfect get in the way of good.
If you’re losing more than 3 pounds per week and/or feeling run down, eat a little bit more protein. 1200 calories seems pretty low for a 200 lb person. If you’re lifting consistently I would expect you to be steadily dropping weight at 2000 calories or even a bit higher. Eat to recover from your lifting but still drop 1-2 pounds per week steadily.