I have a HTC Touch Pro, so well, it's a touchphone, but it shouldn't differ from other Windows Mobile phones. I've noticed that I'm not a fan of the touch features either.
Anyway, I can read all three PDFs from the latest lesson, yes, even including the "non-lite" one, using Adobe Reader LE 2.5. I have installed the Meiryo font on my phone though, so perhaps the Reader is one of those very rare applications that can use it, and even find it on it's own.
Here's how you can install Japanese fonts on your Windows Mobile device:
http://www.ookii.org/software/japaneseinput/font.aspx
Most applications won't be able to use them though.
I don't know about other phones. Perhaps it would be easier to get help if you said what brand you are going to buy.