Hey! No need to apologize! Learned a loooooong time ago that .0 of anything makes users 'omicron testers' (most of the time). Moodle 2 has been a roller coaster ride and with each release, even though there is improvment and they are better, there might also be something not quite right (or broken). This to say, you are VERY wise to work on a test site ... and you are no more 'dense' than the rest of us mere mortals! ;)
Am finding that 2.4.x is like other 2.x releases ... yet another learning experience. Have been helping a gentleman from Austrialia with recovering some 1.9.7 backups from a failing Windows Moodle server onto a 2.4 fresh install. Some success ... some not.
Findings (call them theory and not so shocking): the backup zip you start with makes a difference. Good 1.9.x (any version) backups = better results. That's not so surprising really.
Others may agree/disagree, but here's what I'd suggest ...
The first order of business, once you get the test site up, is to upgrade the 2.0.2 test site to it's highest/most secure/most fixed version in the series (2.0.x). One, supposedly, cannot go from 2.0 to 2.4 in a hyperjump ... but rather, 2.0.x to 2.3.highest, then the 2.3.highest, to 2.4.x.
At each phase, backup (full - DB dump, data directory, code directory) what you have and then that becomes the 'fall back position'.
Since you've mentioned remotely hosted, check with provider concerning support of Moodle 2's higher versions. There are higher requirements as one moves from 2.0 -> See downloads.moodle.org.
Overall, don't think Moodle 2 will run well on shared systems if one has any signficant usage/users #'s, etc.. You might be looking at having to get virtual dedicated server (all your own).
'spirit of sharing', Ken