Congratulations! Now the obsession begins! I've been knitting less than a year, but I think I can help with some things you asked...
Whats worsted weight yarn?
Different yarns have different weights/thicknesses. Some yarns are very fine (like for socks or baby clothes) and some are bulky & thick (this was probably what you used if you used #15 needles. Thicker yarns use fatter needles, finer yarns use smaller needles.
but what difference does the length of the needle make?
The needle length is important for what size piece you're knitting. You wouldn't be able to keep all the stitches for a man's size sweater on a short needle. I'm making little bean bags for dd to try out some new stitches & the only size 7 needles I have are long & it's a bit of a pain because they're awkward to work with on such a small project.
the knit stitch (garter stitch?)
Yes - if you knit all the time it's garter stitch, knittin on one side & purling on the other is stockinette stitch (it's flatter since the bumps are only on one side)
the teacher did the casting on for me
there are lots of ways to cast on, but the easiest if you know the knit stitch is to make a slip knot & put it on the left needle, put the right needle in & knit another stich but don't pull it off, but take the stitch on your right needle & put it on your left. You know have 2 stitches. Keep doing this until you have as many as you need.
and I had my neighbor show me the ending of it
Binding off is pretty easy - knit two stitches, grab the first stitch with the left needle & pull it over the second and off the needle, knit another stitch & repeat the same thing until the end of the row.
I think a book would be my best bet
If you have a craft store (Michael's, AC Moore) they have a kit like I can't believe I'm knitting or something like that. It has needles, counters, a ruler with holes to check needle size, etc. The projects aren't great, but it was about $10 (then a 40% off coupon) & I use all the stuff & refer back to the instructions.
If you're going to a book store you have a couple of options - there are some knitting for kids books which have super easy instructions & pictures and good projects. I also liked the Knit Stitch by Sally Melville which is all knitting (no purl stitch - that's the next book), Stitch & Bitch by Deb Stoller, which has a few less traditional projects.
I've also found my library has great books that I love to look through for project ideas & explanations.
Good luck!!
