Follow the HuggingFace Colab notebooks. They are well-written and language-related AIs are a great way to get started because you'll naturally have a feeling for what it should produce.
Afterwards, do a statistics class. Most algorithms these days are based on softmax, meaning the cross-entropy between two discrete/continuous probability distributions. There's a lot of choice in which distribution to use to model what and it will have strong effects on your gradients and, hence, training trajectory.
Concepts like shannon information and entropy are also very helpful for you to monitor training progress. Typical loss values will do exponential annealing and it'll be difficult to see further progress. But if you still reduce the bits of entropy in your classifier, learning is still going well. So you need to understand what to visualize and how to calculate that.
As for implementing research publications, maybe start with easy mode and go to paperswithcode.com . There, you will find papers AND their source code, so that you can look at how others implemented their paper.
As for FastAI and Kaggle, my personal impression is that it's mostly for toy problems. No real AI researcher would be willing to disclose their full source code to an international megacorp like H&M for a measly $15k in price money, yet similar terms appear to be the default on Kaggle:
https://www.kaggle.com/competitions/h-and-m-personalized-fas...
https://www.kaggle.com/competitions/dfl-bundesliga-data-shoo...
https://www.kaggle.com/competitions/feedback-prize-effective...
EDIT: Also, I strongly disagree with course.fast.ai on these points: "Myth (don’t need): Lots of math, Lots of data, Lots of expensive computers" To train a state of the art ASR AI, you need roughly 100x A100 for a month, 100,000+ hours of audio recordings, and math knowledge to find a maximum likelihood path through a logit matrix. Unless, of course, you're only working on toy problems.