I can understand you feeling overwhelmed...but there's lots of great resources to help you learn whatever you'd like to learn in knitting.
My best recommendations for you:
As far as knowing what to use, if you look on the yarn's label for the little knitting needle picture, it will tell you what size needles are recommend for use with that yarn. That makes it pretty easy. You can use a different size needle and sometimes have to if you are knitting something where your little gauge swatch doesn't come out right (meaning your garment won't fit unless you change needle size and make the gauge swatch come out right before doing the real project), but don't worry about that yet since you are doing a scarf and dishcloth which don't require gauge testing.
The needle size sounds about right for the Homespun...not sure about the dishcloth yarn, but you know what? You are just starting out and learning so don't beat yourself up about choices - just practice getting the basics down first and then you can pick and choose precisely what you want and need.
You can use wood, metal or plastic needles...it's all a matter of preference. Wood is warmer and gets smoother as you use them also yarn doesn't slide off of them the way it can the others (especially important if you make something with double pointed needles later on). Metal points tend to be sharper so it picks up the stitches nicely but are colder feeling and can be slippery. I haven't used plastic but they are lightweight, I know.
I think you picked out two nice starting projects. I would do the scarf first myself since it will go a little faster so you get more immediate gratification.
If you need tutorials on how to get started, go to the video section on this site - Amy's videos are really easy to understand. If you need more help, feel free to ask us (I am a fairly new knitter but you are always welcome to PM me).