How can I train a good posture?

Hi,

I am quite tall for am woman. When I remember to my childhood, I've been always taller than the other girls (and even the boys!). Furthermore I am a quite shy person. Maybe thats the reason, why I always wanted to be smaller and accoustumed myself to walk around with a bad posture, like hanging shoulders and rounded back.
When I became a teenager, my breast started to grow very big and my back to hurt. Fortunately I have found my correct bra size by now, because a well fitting bra disperses the weight of the breast to the chest and the full back. So it doesnt hurt anymore and my back is more upright.
But I think it's also necessary to train some muscles of the back, shoulders and neck, to get a good and attractive posture. How can I do that? Which muscles do I have to train?
I am still a beginner in bodybuilding. I have no gym, where I could go to, but I could exercise with the dumbbells or the barbell of my husband or do bodyweight exercises.