Advice on how to get started for someone a bit later in life?
I for myself wouldn't advise you to not take that route. I do agree with most of the points that were mentioned before but my conclusion is a slightly different one:

Trying to get into data science without any preceding field knowledge deserves respect and it is not impossible. Also, there is still a lack of qualified data scientist and I would predict that the demand is growing.

But you should consider the following points:


Data scientist is probably the job in the statistics/IT area that requires the highest level of education. Ask yourself if this is really what your aiming at. 
If you choose to go on that route be aware that it will be extremely hard. Data science is so multifaceted and interdisciplinary that there is a lot to learn. Even if you'd have a couple of hours to study each day I'm afraid it would take years. Being able to work as a data scientist needs far more than an academical math knowledge.
You will have to compete with PhDs in their mid-twenties who already have years of experience in publishing and conducting machine-learning/math/programming projects. Employers will probably favor them over you.


If you don't care that it will be painful and want to start learning, I'd do the following:


Get basic knowledge of statistics, programming, and IT-infrastructure. You should be familiar with t-tests, ANOVAs, regressions and cluster-/classification techniques. You should start learning a statistical programming language. For starters I'd recommend R or Python. Basic knowledge of another higher programming language is useful. Knowing basic programming principles such as object-oriented programming doesn't hurt either. I'd recommend to take a look at Java since a lot of big data tools such as Hive, Hadoop or Spark are Java-based frameworks. Look at these frameworks, too. Understand what they are used for. At last you should have at least basic knowledge of databases and know the difference between a relational and a non-relational database.
Don't spend money on courses. The internet is full of free sources. Just take into account who offers them. There are a lot of lecturers and professors from very good universities who provide online courses or share their lectures.
Read books. Again: Don't spend money. Search the internet for free high-quality materials (see here for example).
Check out community sites such as Kaggle and join competitions. This is probably as close as you will get to real-job tasks.
Continue doing that for a couple of month and ask yourself again if this is really where you want to go. If yes, continue.


But realistically, here is what I would try to do:


Don't aim at becoming a data scientist right away.
Consider to start in a statistics-related job (e.g. controller, business analyst, marketing manager, game designer etc.) and work your way up. I strongly believe that such a strategy is more likely to be successful. 


Because no matter what you do before starting in the industry, you will have to learn on the job.