As for yarn for learning, I started with Sugar'n Cream cotton. It's a smooth cotton yarn that I worked up into a dishcloth. I cast on something like 45 and just knit until I felt comfortable, then purled, then played with different patterns of knit/purl to see what appeared. By the time I finished a roughly square dishcloth, I seemed to be doing okay. The yarn I used is variegated so it had some visual interest, but it's still plain enough that I can see stitch definition and see where I went wrong.
As for your loose edging, rather than trying to knit with the loop below, just slip the last stitch on a row. If you're knitting, slip knitwise (insert the R needle just like you're going to knit, and slide the stitch off the L), if you're purling, slip purlwise. When you turn you immediately knit or purl that stitch, but this gives you nice clean edges without loose stitches, and a bonus is that it creates easy stitches to pick up if you want to add a crochet edging later.
As for casting on too tightly, I was doing this too. The way I "fixed" myself of this was to cast on, realize it's too tight, frog it, try casting on again, if it's still too tight, frog it again, and keep re-doing it until it was loose enough. It sounds tedious, but it only took a couple times until I got the feel of it. Don't try this with a yarn that will felt though.
Also, when I first started (all those weeks ago ), I had a tendency to choke up on the needles, keeping all the stitches right at the tip, and not pulling the needles apart. This contributes to too tight stitches. Slide the work down so it's on the widest part of the needles and when you slide the stitch off the L needle, pull the R needle away at least an inch, sliding the new stitch down to the widest part of the needle. Doing this consistently has loosened up my knitting considerably.