I think the answer is very much "it depends". If you are a small business then it depends most on who the people are, and what they want to be doing with their time.
If you have someone on your staff who enjoys fiddling around with servers and hosting, then running Moodle yourself is going to give you much more flexibility (e.g. to use any of the many add-ons from the plugins database to extend what activities you can create for your students, or to extract data from the system to understand what your learners are doing). If you don't have anyone like that on your staff, then a fully hosted solution from a Moodle Partner will save you all sorts of worries.
Even if you do go the 'host-it-yourself' route, there are other services you could get from a partner, in which case you might to better talking to a smaller partner. E.g. you might get some consulting from Pukunui to advice on how you should set things up on your own servers, to make sure everything is reliable, backed-up and secure. (I am going by your profile which says you are in Australia, and I should say that sone of the folks at Pukunui are mates, so this may not be impartial, but they do know their Moodle.)
Whether you go host-it-yourself, or partner-hosted, note that at the Downloads link above, you can get Complete install packages for Windows and Mac. You would not want to use these to run a real Moodle site, but they let you very quickly get a working Moodle site on your own computer where you can start experimenting. The Moodle school demo site http://school.demo.moodle.net (which I am afraid is a pretend school, not a pretend commercial training site) also lets you quickly see some of the possibilities. If you want to go more deeply, there are various books you can get https://moodle.org/mod/data/view.php?id=7246, though the free online docs are also good. Another way to learn more, coming up soon, would be to sign up for iMoot http://2015.imoot.org
As for whether Moodle, or some other LMS, would be best for you. Well, Moodle might work well. The "choose your own adventure" bit of your post sounds like a good match for Moodle's Conditional availability: https://docs.moodle.org/28/en/Conditional_activities. Also, have you heard about Open Badges? https://docs.moodle.org/28/en/Badges
Moodle has lots of powerful functionality, which is good, but conversely, you need to learn how to use it. Of course, you can start simple, and only start using the more complex stuff when you find you need it. That is an advantage of buying into a mature package like Moodle, where most of the things that people might need have been added over the years.
Related to the "users stay on the program indefinitely" bit: then as well as thinking the content you want to create an host on the site, you might also want to think a bit about community. This is an area where Moodle does very well. This 'course' on moodle.org (if you can call it a course) consists of little more than lots of different forums, but plenty of us keep coming back here, and learning from each other, even without any provided content.
Hopefully some of that is useful, and I have not just confused you even more by suggesting even more possibilities to consider