Finally, after making sure I had the right packages and the proper stuff installed, I managed to set up SCIM for one of my Ubuntu newcomers as it should be, properly snapping to hiragana, and switching straight to kanji when necessary.
I wish I could say exactly what the problem was. I had set and reset so many different options in the SCIM panel that to be honest, I really don’t know what was original and what was somehow changed. I know for a fact that the first time around I didn’t have scim-anthy installed, so that might have made a big difference. But after that, I can’t tell you (or me, for that matter), which button made it work right, the first time.
It’s a little frustrating, since I’d like to be able to refer to that later, if I ever have to set it up again. But it just means the next time around I’ll have to relearn it all like new, which really can’t be any worse that what I went through this time.
I do know that it made a night-and-day difference in how the computer user felt about Ubuntu. Where Linux was a curiosity and a gimmick until today, it’s now seems to be the preferred OS between that and Windows. Which is good; I believe the chance of it “sticking” will be higher this way. 
Way-Hey! Glad you got it sorted.
Anthy is what actually does the character conversion, so I think you’ll definitely need scim-anthy to interface (and Anthy itself of course!).
If you do a search for “japanese” in Synaptic you’ll find some other japanese input methods that work with SCIM, but I haven’t tried any. Anthy seems the most popular.