It helps to have some level of understanding of the chemistry. It can be hard for anyone but a legitimate chemist to sniff out the bullshit in academic papers (I've fallen prey to this before; I'm just an electrical engineer).
Raw materials can be important, but only very rarely and it can also be misleading. By far most of the cost comes from the complexity and time of manufacture. That makes it tricky. For instance sulfur is far cheaper than other anode materials, but there will never be a cheap sulfur battery- it's way too complicated.
It helps to know the basics[1] of battery manufacture: it's a decades old process and highly optimized. The gist is that you apply coatings to a reel of tape. If it sounds like it can't be put on a tape very easily, it will probably fail the sniff test. Solid/ceramic electrolytes and most kinds of nanotechnology fall into this category. Coating a tape is cheap, but using an electron microscope or laser on every battery is not.
>2. Charge/Discharge cycle count - thermal and mechanical stresses
>3. Power to weight ratio; power to cost ratio
Critical. Any article, paper or press release will stress the interesting part of the battery; it's up to you to figure out how relevant it is. If the article emphasizes the current capacity, check the voltage of the chemistry. If it emphasizes the energy density, check the power density. If it emphasizes the weight, check the size. If it emphasizes safety, check everything. This is often nontrivial though. It's possible to tweak your numbers to balance things out- if you scale back the storage level you can increase cycle count, etc. If a paper has improved everything, it has a shot at being a next gen chemistry. Of course it may also be bullshit.
In my experience just remembering to check the other attributes of the battery will weed out 90%+ of bad articles. Most people are honest, they're just obligated to play a certain game to keep their funding up. Unfortunately there still are folks who will publish garbage though.
[1] https://www.youtube.com/watch?v=HJrNCjVS0gk