One thing to note is that you are not expected to be aware of every daily news story, or to memorise the details of many stories. What is more important is developing an ability to think commercially, which is thinking about how the news is relevant to firms and clients as you have mentioned, and just being aware generally as to what is going on in the world.
If you are finding it overwhelming, I don't see anything wrong with reviewing once a week as you have suggested. In fact, this might be preferable as you can sit down for longer and focus on the biggest/most relevant stories only. It may also be more time efficient if you can review all of the developments of a certain story in one go, rather than reviewing over and over as things change on a daily basis.
I wouldn't recommend focusing only on one practice area. I personally think it is good to have a broader understanding of current events and that having a wider overview can help you develop your commercial thinking faster. I would therefore suggest spending time understanding both general events, and the events that specifically impact your target firms/areas of interest.
In terms of approaches to staying updated, you could think about the ways you enjoy consuming content and what you find easiest to digest. I personally love podcasts, and there are tons of daily news podcasts out there (BBC Wake Up To Money is my favourite - they break things down and explain how stories impact individuals/businesses). I find it easier to fit a podcast into my day, instead of sitting down to read a news website. Other formats may include YouTube videos or following other news platforms on Twitter/Instagram. You should also follow prominent people in your practice areas of interest on LinkedIn - lawyers often share their comments via LinkedIn posts.
To see if you are hitting the right ideas, you can brainstorm the implications of a news story independently first, then check this against the commentary online (i.e. TCLA commercial awareness articles, articles on firm websites, Lexology). You may find that other sources will raise new points for you to consider. Discussion with peers is also a really good way to see if you are thinking along the right lines and exchange ideas. You could try form a group with others who are interested in developing their commercial awareness and hold e.g. monthly discussions, or discuss on the TCLA commercial awareness threads.
Also, if you are doing what I outlined in the above paragraph, you are learning how to analyse the facts from a commercial perspective, so even if you can't remember these stories again in a months' time, you will have still gained something from doing this analysis.
For an AC, I would probably prepare 2 to 3 which are relevant to the firm/of interest to me, although I'm sure other members of the forum can weigh in on this with what they think is best!
Let me know if this helps