Well, Moodle 1.9 can do the job even if newer versions are better and currently supported. I'd suggest to check whether you can upgrade it to 1.9.16 or 1.9.17 which fix some issues, though.
In terms of producing and administering quizzes, you have at least 3 different modules, Simon, that you can use in Moodle 1.9: feedback, quiz, and questionnaire. Each has its pros and cons and varying sophistication. You can of course mix and match them to your needs.
In terms of a simplifying the user navigation, you can eliminate one click by displaying the login page right away (normally, the front page
is shown and users need to click to login, unless you insert the sign-in block, which is fine but users need to orient themselves on the page to see it). You can further activate the MyMoodle option, so instead of the normal front page for logged-in users, all they see is their course. This saves no clicks but reduces the interface to minimum.