If I can say something, I don't understand why Lomaster thinks Microsoft's IME is a must. I've never had any problem with any IME I've used, and I can guarantee that I haven't used Microsoft's IME in... almost a decade, probably, because I'm exclusively a Linux user and typically use Anthy. I was probably using Mozc at one point as well, though (Mozc is an open source variant of the Google IME), since it's another popular one for Linux.
Every single entry method mentioned in this thread, by the way, works in my usual IME of choice, Anthy (and for the record, I only have an IME of choice because Debian doesn't have one installed by default; I have to install the ibus-anthy or ibus-mozc package, and ibus-anthy is just what I've always picked). I don't think Mozc fares any worse and I don't see any reason to think the Google IME would, either.