I started with weaving towels using 8/4 cotton. The good thing about those is that there are not as many warp ends (200 vs. 400), so for me it was less intimidating than 8/2 cotton. I also used a short warp length (3 m). The second project I made was a scarf with 8/4 cotton as warp, and knitting wool as weft. That was fun and allowed me to use up some of my knitting wool stash. I think from now on those scarf projects will work as a palette cleanser for me in between projects, or for when I want a quick gift or something mindless.
I am going through season 2 right now and I completely agree that the first sample is a really good beginner project, but I was intimidated by putting on such a long (to me anyway), warp. Working with the 8/4 towels gave me the confidence I needed to tackle a 6 yard warp in 8/2.