However, when sitting, I use an external mouse and keyword, and use my DnD starter kit and a few books to raise my MacBook to eye level.
This keeps me sitting up, but doesn't fatigue my hands by keeping them raised.
The only thing I regret with this setup is buying a bloody magic mouse. Just don't buy it.
I have used the 5x5 program and while I'm not here to endorse any particular program, I found that I really liked it. It did help me learn proper form, as you say, and it also gave me a very regular workout. I had it memorized and it always uses the same part of the gym (squat rack) so it helped me maintain a rhythm.
I actually built a squat rack at home eventually to start it back up after some time away.
There may be better programs, I have not actually tried any others. 5x5 was the most-recommended I found in my research a few years back.
Also, GGP, lifting did correct my posture very quickly. People kept telling me I looked taller/stronger/wider even before anyone knew I was working out (and before I had actually gained any muscle), and I'm quite sure that was just my improved posture.
The other thing for me was it started to take too long - I generally try to get my stuff done in an hour or so before work. I went from SL to GSLP to 531 (3 main lifts, to 2, finally to 1, per session).
To be honest, I don't think it matters too much - as long as you find something you like to do enough to stick to regularly, you'll improve in health and posture either way.
I always found that I could get my lifts in in about 45 minutes. It can be slower with a partner if their weight is very different from yours, because you're moving weight on and off a lot the bar, but ours was small enough that it wasn't a major time concern.
Later I did it solo and my workout times were ~30 minutes for the quick day, and ~45 minutes for the long day. The long day being squat/bench/row, and I felt like my breather periods were very generous.
I personally do squats, deadlifts, 3 minute planks at the very end of workout ('finisher') and other exercises where core is a secondary, stabilizing muscle (pullups, running etc).
For start I would recommend something with body weight (pushups, planks), simple and easy to do, and focus on many repetitions. Much safer than trying to push to your max and injure something in your back with long recovery.
It's a mistake in training to focus only on one part of the body. Over time developing all muscles helps tremendously with any activity/sport.