Deadlifts and squats. If you're a newbie, follow Mark Rippetoe's "Starting Strength."
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.