Hi ThinkGod1! Working your postural muscles is 50% physical exercises and 50% awareness of how you stand. Just making a better effort to stand up straight will improve your posture immensely. Even if it means you have to put up stick up notes saying "sit straight/stand straight" all over your house and car too (driving is when many of us tend to slouch).
As for exercises, working your core (lower back region) is essential because those are the muscles that will keep your deep abdominal muscles and low back muscles strong. If these muscles are weak, they will tend to "collapse" and pull the shoulders into a rounded position, which in turn makes the neck suffer as your chin juts forward.
To work your core do planks. All versions of them (straight arm, on elbows, reverse planks etc.).
To redirect and correct rounded shoulders, focus on maintaining a scapular retraction when doing applicable exercises...exercises that work the rhomboids, trapezius, infraspinatus, rear delts, and external rotators (back and shoulders exercises)
We touch many of these areas in the Gym style workout you have but you may also want to take the band and do additional work.
Hold the band out in front of you overhand grip and draw both arms straight back and out to the sides of your body so that the band stretches over your upper chest area (15 times holding for 5 seconds while stretched out). Repeat this again with an underhand grip on the band.
Also, keep your arms bent 90 degrees at your sides holding the band with about a foot of distance between your palms up hands. Pull the band from the center toward the outsides of your shoulders for an external rotation (15 times with a 5 second hold when stretched out).
Hope this helps