1. Find out what kind of information that is wanted from the model and what kind of data you have available that could help with this. 1b) And note down other requirements for the solution.
2. Find out how to formulated the information needs in terms of a well-understood and well-researched problem.
3. Find out what the current best performant and well-understood solutions are for this problem. Usually through a literature search.
4. Choose a few candidates, and rank them wrt your particular requirements.
5. Test out 1-3 of them
This is a business-needs-first, top-down type method. Prior knowledge of the details of a lot of algorithms not needed. Ability to understand terminology and quickly identify relevant material/papers critical. A good overview of common problem formulations and methods will build over time, and speeds things up immensely.
But I agree I wish there was more resources on that, it seems to be just a trial and error process.
Anyways I had to research a little into the subject and what I found is that there isn't a straightforward approach to choosing algorithms. I could be mistaken, but I believe the best approach for you would be to get intimate knowledge from every ml algorithm and maybe use a cheatsheet to guide you, but ultimately only knowing well your data set (distribution of classes, occurrences, which traits are better for which categorization you want to do etc..) will bring you farther than looking for a recipe for choosing an algorithm.