Tis the season when the temperatures sometimes dip low enough to freeze the water in the drain of the dishwasher, so that it can't drain. Yuck. (Our landlords have some insulation issues back there to address.) This makes handwashing dishes much more attractive. My long-term house plan doesn't even include a dishwasher. I dislike bending to load and unload the dishwasher, and if you add up all the effort that takes, it does not even save much work over handwashing.
So, handwashing dishes requires dishcloths, and dishcloths from the store are not all that great. I have knitted my own for many years, and they work very well and last a long time.
Nearly all directions will tell you to use cotton yarn. The advantage of cotton is that it doesn't melt, and therefore can be boiled for thorough sanitization, or used to scrub very hot pans. But since I never do either of those things, I have found that acrylic yarn works just fine. The scratchier, the better.
Some of my dishcloths are just squares of garter stitch. Some started with a small square, which I enlarged in various directions by "knitting on"--picking up stitches from an knitted edge, and knitting in that direction. I also experimented with making a more traditional diagonal dishcloth with eyelets along the edge. (There is a good free pattern for that here.) I am thinking of making some more with fancier lace stitches. There are options for every skill level.
And there is no reason why dishcloths can't be crocheted. I just prefer knitting.