This is the first time I'm modelling a hierarchy within the same model (product categories).
I found a great post on this topic. Since I use Rails 4 & Postgres, which according to the article supports recursive querying (this is the first time I hear this term), the "Adjacency List With Recursive Query" seems to be the way to go because it's both easy to model and fast to query.
The article suggests the acts_as_sane_tree gem, which supports recursive querying. This repo hasn't been updated for two years and I'm not sure whether it supports Rails 4. The project is a fork of the acts_as_tree gem, which supports Rails 4 and is well maintained.
Which gem should I use? And does the acts_as_tree gem support recursive querying to avoid expensive queries?
If you are in doubt what gem to use, I always suggest to takes a look at the Ruby Toolbox. It helps to evaluate if a gem project is still active, how many developer using this gem and a lot more. Why do you know to do that? Do do not want to choose a gem that is not maintained anymore. You want to use the tools that the community uses and stay as close to the mainstream. If you do not follow the community you will run into problems if you need a bug fixed, further documentation or want to update your Rails version.
In this case for nested ActiveRecord awesome_nested_set and ancestry are good candidates. I would not choose the Recursive Query implementation, because most databases do not support this. Unless you have a very good reason, it is not worth to bind your app to a specific database management system.