Battery holders (AA, AAA, 9V), maybe some op amp chips, CMOS decade counter and multiplexor chips. Gotta run now, I might think of some other things later.

Why don't you need a variety?

Because I'm biased. I'll actually admit now that I was wrong- I tend to work largely in the digital world, so most of the time, I only need those three values. An assortment of mylar or poly caps is actually very useful if you're going to be doing analog design, particularly stuff like audio. Don't get electrolytics or ceramics- those are not as useful for general purpose applications.

The selection of the capacitor technology to be used in a particular application can be very confusing. I'll try and cover it a bit in the class- Horowitz and Hill provide a lovely chart in "The Art of Electronics", which is basically a degree in EE in a book.

Dang, I thought you had some deep EE secret to share about caps.

I wish there were some deep EE secrets, but I don't think there are any.