So for anyone getting their mind around the discussion in this thread as I have just done, I will sum it up here. (Thanks for your help Gordon.)
The goal here: to force students to go through a TaskChain in the order without the option to return to a task through the tasks menu. A TaskChain is a set of Hot Potatoes lessons (among other types) put together into a lesson and the grade will appear in the Moodle grade book.
Using the Edit Tasks menu on my TaskChain of three tasks, the conditions are shown. More complex conditions are possible such as the required scores on a task and more.
In Edit Settings, I have allowed unlimited attempts and I force "resume". With the conditions above, putting "yes" in resume functions the same way. "Allow free access" is set to "no."
It means that students will be able to resume a TaskChain but will resume at an unfinished task or at the next one they have not yet attempted, even if that attempt was nothing more than a look at the Task without any interaction.
Also in Edit settings, you see the grading system chosen for the mark book. I would usually have the category chosen too. Highest grade means that the highest grade achieved on a complete TaskChain is the one that will show in the grade book.
You can see my 8 attempts on my test TaskChain and the options available to me as a student.
Lots of powerful options here. Please let me know how you would do things differently.