Mira

The most famous variable star. Also known as Omicron Ceti. It has a period slightly less than 1 year, and the magnitude is usually 3 or 4 at maximum, and 9 at minimum. Although it can be seen with unaided eyes during maximum, I recommend a pair of binoculars to see the comparison stars clearly. A small telescope is needed during its minimum.

I followed its brightening in 1998 and 1999. It is the kind of quick project: when the sky is at least partly clear, take a look and write down the time and magnitude estimation. It takes less than 5 minutes. Do it on different nights. I did this for 5 months, until it set too early to be observed. Here's a plot:

As can be seen, this year's maximum is not very bright. The peak is somewhat flat.