I don't know a whole lot more than you, but I have one whole scarf and several aborted ones under my belt so I will offer suggestions for what worked for me.
First of all, the idea of a scarf without a pattern is a terrific way to start - all it is is a flat rectangle, and i don't think it gets any simpler than that, but the finished product is still something real , so it isn't a dinky practice swatch.
I first tried Caron SimplySoft (100% acrylic) yarn with size 8 Boye needles. The yarn and needles are a decent match, however, if you are doing garter stitch (just knit stitches, no purls), I would caution a little patience and tolerance for errors. I found that that combination showed inconsistent tensioning very readily, and I would imagine that everybody tensions inconsistently during the early learning phase. What this means is that some stitches are longer than others, and the garment looks uneven. The bottom half of the one I tried this way was probably only 80% as wide as the top, which looked ugly.
The scarf I finished was on size 7 bamboo needles with Paton SWS yarn. I would not recommend the yarn for a first project - although I finished mine and am happy with it, the stuff is a real pain to work with, and I spent as much energy wrestling with the yarn as I did focusing on learning the stitching, which is what my main focus should have been on such an early project.
My recommendation for your scarf is to use size 8 or 9 aluminum needles and either Caron SimplySoft or an easy to work with wool yarn such as Paton merino. If you use the Caron, it might b a good idea to do your scarf in stockinette (alternating rows of knit and purl stitches) to avoid the above mentioned tensioning problem, because I think stockinette is a little less susceptible to that problem than garter stitch it. If you do go that route though, read the stickied thread in the how-to section regarding stockinette stitch and curling.
Again, I'm certainly no expert, and there are like a thousand helpful people here who know way more than me, but I was thinking more or less exactly like you a month or so ago, so perhaps my experience is helpful to you. Good luck and don't stress!