Okay so....the easiest thing to learn, in my opinion, are the double knit scarves (sounds complicated, but is actually super easy. For those all you need is a long/rectangle loom
like these. And either the stockinette stitch or the twisted stockinette/figure eight stitch. (I'd link to videos, but my phone won't let me checm YouTube
..
I would also recommend the new fine gauge round loom set. (
Link Here) The original ones are such a big gauge that you practically need to use bulky and super bulky yarn for everything, but the fine gauge ones would work well for worsted weight yarn.
Also, most kits generally come with a little booklet that has some basic project patterns, but I like the authentic knitting board for a lot of new patterns (mainly in the blog sections). They do mainly have patterns specific to their looms, but they have a good section of beginner instructions (
here) as well as a series of Stitchology lessons that helps learn new stitches and has actually helped me to learn how to read a pattern chart.