I have been doing weighted squats for about 6 months now and oh my god I am so happy with how big my butt is. I cannot wait for it to become even bigger by next year as I continue doing squats.
If you're really interested in those butt gains, look up Bret Contreras aka "The Glute Guy". He posts some workouts on Instagram (who doesn't these days?), but he knows his stuff.
Barbell hip thrust and bulgarian split squats, if you really want to work those glutes. Squats and deadlifts are great, but always try to include some bilateral work (eg bulgarian split squats and lunges) and exercises to focus on specific muscle groups (eg hip thrusts).
Generally the advice is to strengthen your lower abs and glutes, whilst stretching your psoas and hamstrings. But I still have very pronounced APT whilst having very strong glutes and decently strong abs, which tells me that I still have a lot of stretching to do.
What do you mean by computer nerd neck? I do shrugs, which hits the traps, but I find my neck is a bit thicker too.
Front squats isolate the quads more - I prefer to do back squats, then isolate smaller groups with quad extensions and hamstring curls; the latter being good for the glutes too.
Stretch your chest muscles, do face pulls. Do rows and deadlifts. If your posture is really bad, don't train (strengthen) chest until you've improved things a bit and have done plenty of stretching.
Then use postural reminding aids (don't use a brace unless a physio tells you to), I put a small massage ball behind each shoulder blade and the chair when i'm working, if they fall I know i've slouched.
I went from people openly telling me I needed to fix my posture, to being credited with great posture in about 4-6 months. My posture actually still needs work, because I have pretty noticeable anterior pelvic tilt, but the forward-neck issues are mostly gone.
