Ok I'm only 26 but I just started dancing two months ago just for social purposes only (a new option to have fun and so I wont be the one person standing at the edge of a room at a function).
In my group lessons I dance with quite a few people your age and they are doing great. We all have pretty much the same problem with posture regardless of age.
Lessons move at a pace that allows your body to adjust so if you are only in it for the joy of dancing you should be fine without worrying too much about extra exercise.
I am relaxedly working out at a gym now: shoulders and back to stop my shoulders from slumping forward is what seems to help me the most.
A bad posture will tire you and your partner more than anything I have found.