There are a lot of very fundamental/general concepts that apply to pretty much any domain you want to think in, and they can be some work to acquire, but are also worth it. I think the greatest value I got from reading in mathematics (especially history of mathematics) and philosophy was familiarity and practice with some of those most general terms/concepts. Things written for 'the intelligent layperson' tend to make heavy use of these terms/concepts (since they can't rely on the particular jargon of the field they're describing); so you'll pick up more by reading things that fall in that category. It's a decent bit of work depending on your background, but I'd recommend working through Eddington's Philosophy of Physical Science —if I had to choose one. It's not too long, consistently interesting, and focuses a lot on exactly the sort of general terms I've been talking about; e.g. there's a chapter getting at the meaning of 'structure'.
But perhaps more importantly, people tend to underestimate how specialized their practice is—or how little it generalizes rather. For example, if you want to get good at writing computer programs—the best way of doing it is to spend your time writing real computer programs like the ones you want to be able to write well. Spending your time practicing by doing anything else will fall short of that.