If you are interested in a career in algorithmic trading, I strongly encourage you to formally study math and computer science. Algorithmic trading firms have no need for employees with financial knowledge; if they did, they'd just be called "trading" firms. Rather, they need experts in machine learning, statistical modeling, and computer science in general.
Of course there are other avenues of employment at an algorithmic trading firm, such as accounting, clearing, exchange relations, etc. If that's the sort of thing you're interested in, again you'll probably want a formal education in those areas as opposed to just reading about finance in the news.
If you edit your question or add a comment below with information about your particular background, I could perhaps advise you in a bit more detail.
Given your comment, I would say you have a fine academic background for the industry. When hiring mathematicians, firms care most about the ease with which you can explore and extract features from massive datasets (especially time series) regardless of what the dataset might represent. An intelligent firm will not care whether you arrive at their doorstep with zero finance knowledge; they will want to teach you everything from scratch anyway.
Nonetheless, some domain knowledge could be helpful, but you're not going to get "more" of it from reading any mass market news source, whether you have to pay for it or not. That's because
- a mass-market news source, no matter how "in-depth" or specialized its coverage may be, will not even scratch the surface of the body of information you will need to learn once you're employed in the industry.
- an in-depth news source is going to assume you're already familiar with all the technical jargon and historical context. A less in-depth news source may actually be better, as it will often rehash primers over and over again to make sure everyone in the audience is up to speed.
Some non-mass-market news sources in the industry are
These are subscription-only and actually discuss real information that real professional investors care about. They are loaded with industry jargon, they're extremely opinionated, and (in my opinion) they're useless. I can't imagine trying to learn about the industry from them, but if you want to spend money for news in order to be exposed to the innards of the industry, then either of these is far better than the Financial Times. Despite requiring a subscription, the Financial Times still does not cover the technical details of professional trading.
Instead of trying to learn from news, then, I would suggest some old favorites:
and, above all else,
Read everything in the navigation box on the right side under Financial Markets and Financial Instruments.