Typing Club https://www.typingclub.com/ is a free program to teach typing. You can go directly to this URL to access it, and it is also available free in the Chrome web store.
Their “selling points” are that you can log in from the same URL, you can get great reports, you can adjust the difficulty for your class or for your individual students (e.g. words per minute in order to complete a lesson; % of accuracy), you can limit the number of lessons students complete per week, and whether or not they can see a class chart (to encourage competition). These points are geared towards classroom instruction.
You have to wade through a lot of advertising to get to use this site. What you see eventually is a page with letters, which the student types. Depending on the accuracy or time with which they type, they are awarded stars. They can go back and keep trying until they get to 100%, when they will receive 5 stars! A nice feature is that you can view the “hands” on the keyboard, or turn them off so the student does not see them. This helps students find the correct keys.
I did not see any supplementary materials or games for students to work to achieve greater mastery. However, if you want to find a free typing site, this one would be helpful.
Here is a screenshot of a typical page, including the ever-present advertising: