All vowels are soft/short ( a = ah not ay, I = ee not aye).

R's get a slight trill/flip -- like Spanish, but less pronounced.
Think of it as sounding halfway between R and D

What are some of the other words you've learned so far that illustrate the sound of the vowels?

About that "ou" at the end of "Arigatou". Why not just "o"? Because in Japanese it's written " a ri ga to u"
The "u" is actually pronounced, but it's hard for us to distinguish between "o" and "ou".
Because there are different systems of "romanizing" Japanese, you might see "ou" or "oo" or "o" with a bar over it.