Joomla is suppoEted for sure, just get sure to upload it in the ZIP you download it from the official site, as if you upload it file by file, some may get lost in the transfer.
Then, you just need to follow the instructions provided with the manual.
for example i am very glad that autoinstaller here does not install Joomla 1.5 as it doesn't have enough features (extensions,components) designed for it.
However it's a matter of taste, so I'm going to publish a short tutorial "How to install Joomla manually".
With this you can install any version you like.