Bad posture is also a symptom of a greater muscle imbalance or weakness, not necessarily something you should focus on changing on it’s own.

I had very bad posture, but once I started going to the gym and strength training and built a more balanced base of strength, my posture improved greatly on it’s own. At least I have noticed significant difference.

Hunched shoulders can be corrected somewhat just by exercising the back with pulling exercises like lat pulldowns, pullups, and rows.

Lower back issues can be helped by training dead lifts, good form for that exercise is extremely important though.

Of course you should also include some yoga and stretching in your routine too, that has numerous benefits. I would recommend getting a personal trainer if you’ve never been to the gym before to teach you to do exercises correctly until you’re comfortable on your own.