Years ago an old lady showed me how to crochet a diagonal double-sided potholder I've never seen in any pattern book, and they're great! They're a bit boring to make, but look good, work well, can be any size you like, use up odd bits of yarn, have no ends to weave in even if you change yarns frequently, require no increases or decreases, and need only one seam to stitch the thing shut.
How to do it -- decide how big you want the finished square to be, and measure the diagonal. Make a chain that is the length of the diagonal without stretching (and it doesn't matter if it's an even or odd number of chain stitches). Do a double crochet stitch in every chain all down one side, and then just keep going down the other side of the chain. It will seem "wrong" since you're not doing anything special at the ends of the chain and will probably seem stretched or tight, but that is correct. Now just keep on going round and round and round, etc., with double crochet stitch. You can go through the front hoop or the back hoop, but once you decide, keep doing the same. After an inch or so you will notice that the ends want to fold in, and that's what you want. Keep on going, and let it fold in on itself. When it gets big enough so that it looks like the folded halves will meet, put it on a flat surface to see whether you need to add another round or two. When they meet, go to the end (don't worry, you'll see it), stop work, lock the last stitch, and cut off a tail of yarn long enough to stitch the seam shut. Stich the seam, leaving the tail inside, and you're finished! You will see that the stitches are all diagonal one way on one side, and the other way on the other side. You now have a double-sided pot holder (or trivet) that protects your hand from heat and that can be tossed into the washer and dryer.
To see if you like doing this sort of potholder, I suggest you make a chain of about 15 stitches and make a little bitty one. (You can stuff it with old scraps of yarn or with batting scraps and call it a dollhouse pillow or a pic cushion if you like.)
As to yarn, worsted weight works best. Use any hook that pleases you and feels right with the yarn. You can use just about any crochet stitch you like for the body -- single, half double, double, etc. I prefer double since the work goes faster -- as I said, this can get boring! -- and the finished potholder has a good "heft" without holes to let the heat through. I am not a fan of variegated yarn, but it looks wonderful with these potholders, and you can get 3 large potholders from one 4 ounce skein. You can make stripes very easily, but you might want to make one without stripes first so you can see how you will have to shift where you make the yarn changes so the stripes begin at the edges.