Hi welcome to the forum. I can help you out with a couple of your questions.
First of all , I believe the reason you are not felling sore in the shoulder blades / back is because your back is such a large muscle. Yesterday I was pretty much lifting my own body weight for a couple of back exercises, today my back is fine. A little tight, but that is only because I need a good massage!
When you stand up, lift your shoulders up then back. This will get you started.
I have found my posture has improved massively due to my weight training program, as evidenced in the photo journal section, (backspace’s progress). Take a look.
However if you want to improve posture without building muscle, I would recommend Yoga. I don’t know it might just be me, but I think this would suit you best. I think you would really like it, you wont have to buy new equipment, or pay a gym membership.
Yoga has heaps of benefits outside of improve posture, it will improve circulation, blood flow, and even free up your “chi” energy.
Even though I don’t do it much, I am a big fan of body resistance training. Try doing 1 set of 20 push ups in the morning and build up towards two sets.
With your dumbbells, don’t make the mistake of trying to just train one part of your body, if you really want to build some bulk you need to lift heavier weights for shorter reps and have eat more calories than you burn.