You're never too old to start ballroom. Whether you will reach your goals, or not, depends on what those goals are. If you can't afford to pay an instructor, it's likely you won't be able to pay the expense of competition either. However most people find social ballroom very enjoyable, and that doesn't require competition, and that should be within your reach. Not being able to accomplish something because the body doesn't want to cooperate can be a little frustrating at times, but I'm sure you already know that. Just don't expect to look like the top level competitors and don't set your goals so high that they are unreachable.
I wouldn't start ballroom with samba. That's more difficult than some of the other dances and it isn't used as often. As a beginner you will get more mileage out of waltz, foxtrot, east coast swing, rumba, and cha cha. I would recommend starting with those. There are no problems with starting the learning process with more than one dance at a time, although I wouldn't recommend starting with all of those at once.
If you can't afford private lessons, consider some group lessons. Those are a lot less expensive. If you try to teach yourself, you won't be able to see your mistakes and won't even be aware of them. You could video tape yourself and compare that to a tape you might have, but when they are different, you probably won't be able to figure out why. That's where some help will be very valuable. You will need a partner (or someone to dance with) when learning. Dancing solo is not even similar to doing it with a partner.
