Practical Crocheter wrote a while back about how useful kitchen cloth is, and how easy to make. They are the perfect beginner project: imperfections are largely irrelevant; dishcloths and potholders are useful; they can be made from plain, worsted weight yarn; they are small, quick projects; they are a great way to try out new techniques and stitches. But here's another idea. You can use kitchen cloth as a place to learn how to use small yarn or thread.
When my father-in-law cleaned out his late parents' house, he gave me all his mother's needlework stuff, including her embroidered kitchen towels, crocheted doilies, and potholders. Some I use. Some need finishing. Some are in bad enough shape that I just look at them. One potholder in particular, though, sees a lot of action. It's made from number 10 crochet cotton. It has nothing interesting going on for it--just a double thickness of double crochet, probably with a size 7 hook. I think it was intended to be used as a hot pad on the table.
This hot pad would never be useful for pulling things out of an oven, and I don't have much use for trivets these days. Instead, I use it for pulling glass containers out of the microwave. Many of my containers get hot in the microwave, but my regular potholders are too bulky to use there. This thin, thread potholder, however, is perfect for tight spaces.