I'll second m_goldberg's concerns regarding the scope of the question as asked; however, getting students more acquainted with Mathematica such that they can use this tool to solve problems important to them is a task about which I feel very strongly.
Because I view Mathematica as a tool (one I enjoy using), I view your question similar to this one: How to teach Hammer. Grammatical liberties aside, my point is that tools are objects used within the context of something bigger, and are rarely, if ever, taught as standalone skills. Consider how you might entitle a course that contains a module on how to use a hammer; for example, Intro. to woodworking. The course is indirectly about how to use a particular set of tools to create something out of wood.
Likewise, I find it is much more productive to teach Mathematica with a purpose in mind. In my case, I want students to use Mathematica to visualize and process data collected in their (real and virtual) Chemistry laboratory experiments. Since they have a goal (e.g. create a plot of your first order kinetics data including a linear regression line), they have a clear path guiding them towards their goal. Mathematica is huge, it's syntax is not intuitive to those unfamiliar with programming, so it is very easy for beginners to get lost.
Others will disagree with my perception of Mathematica as a tool rather than a language and point to a standard Computer Science curriculum, where courses in programming C, Java, Python, etc. proliferate. It's also clear that WRI wishes for us to accept the Wolfram Language branding. My primary issue with this approach is that I do not believe teaching someone how to program in the Wolfram Language is as valuable as helping them learn how to solve problems.
In summary, if my students were asked the question, "How comfortable are you with using Mathematica?", I would like them to be able to answer with something similar to, "I used Mathematica to analyze data that shows how bleach will remove blue food coloring at twice the rate as it does red food coloring" rather than a generic "I can use it to perform linear regressions".
Off the soap box, answering the question
Here are a few examples of times where I have exposed my students to Mathematica.
Using custom-made CDFs and objects from the Wolfram Demonstrations site: Students gain an appreciation for the power of Mathematica, and based on how well the CDF is designed, are able to meet the learning objectives of the module. Naturally, they gain zero understanding of how Mathematica was used to design/present the information. Nonetheless, I use this platform most often as it is best suited for my student-base, which is typically computer-programming illiterate.
Formal instruction. I create videos and worksheets for students to view and follow in order to complete their project objectives. Even the stronger students in my classes tend to treat these materials as cookbook instructions, and the weaker students inevitably "borrow" notebooks to plug in their own data.
Opportunistic instruction. In several instances, I have had students ask me how to do something in Mathematica. Most recently, given that my institution has decided not to renew its license, is how to use the Cloud/Development platform. I started some screen-capture software and walked the students through the process, then gave them access to the screencast. Two of the three students continued to use the Cloud for other projects.
Independent learning spaces. My research students make use of Mathematica in their work, and since they have very varied projects, it is difficult to have a one-size-fits-all worksheet/introduction. Instead, I teach them about the resources available such as Stack Exchange and how to effectively use the documentation. It is a tedious process; however I see the most improvement in Mathematica proficiency in these students.
The short version
Now that I've worked through my ideas (hopefully for someone else's benefit, but I suspect this exercise was most beneficial for me), I think I can more succinctly answer your original question.
There is no one set of questions/resources that I find most beneficial for teaching students how to use Mathematica. I prefer a problems-based approach in which the students have a problem to solve and learn how to use tools (in this case, Mathematica) to solve the problem. In my instructional delivery, I help students learn how to search the available resources for guidance. I encourage students to "'Google' linear regression in mathematica" rather than pointing them directly to a particular Q&A or documentation page. Students then benefit not only from the in-context-learning, but also gain tangential experience in searching for and critically assessing resources available to them. It also has the added benefit of removing some biases in my instructional delivery, since I am suggesting resources as an experienced user trying to remember how I felt at the start of the journey.