Welcome to the amazing world of knitting!
Here's a basic run-down, using examples from Lion Brand (lionbrand.com):
Weight - This has to do with the diameter of the yarn. Different yarns are labeled differently, but mostly it's laceweight, fingering, sport, worsted, chunky, and bulky, from smallest to largest.
Types - There are lots of types of yarn available, to say the very least! There's your average plied yarn (like WoolEase), what most sweaters, etc. are made of, which has two or more plies (strands) of fiber wound together. Boucle is yarn that has nubs or bumps in it (like Lion Boucle or Homespun). Novelty yarns can be all sorts of things, from Fun Fur to ribbon yarn (like Incredible) to ladder yarns.
Fibers - Every knitter has his or her favorite fibers to knit with.
Acrylic is generally cheapest and is machine washable, but doesn't breathe well. These days, there are all sorts of acrylics available, some good ones and some not-so-good ones.
Wool is a little more expensive, but it breathes better. You can get superwash wool if you want to be able to machine wash your finished object. If you wash non-superwash wool, it will felt. (You've probably done this without knowing it - like when your dad sticks your 100% wool sweater in the dryer and it comes out Barbie-sized.) Wool is a little more elastic than acrylic or cotton, so a garment made from wool will retain its shape well.
Cotton is lightweight and washable, but it doesn't stretch well. If you're a brand-new knitter, it's probably best not to start with cotton, since it's harder to manipulate until you get used to it. Making large fitted garments from 100% cotton isn't always a good idea, because the weight of the cotton will make it sag. Blending cotton with a synthetic fiber like acrylic or with wool will help with this problem.
As to what type of yarn you'll need, that depends on your project. Don't start out making a duster-length sweater with laceweight yarn unless you really enjoy knitting...and knitting...and knitting...FOREVER. Likewise, I'd recommend not making socks in chunky weight yarn if you want to be able to wear them with shoes.
For a new knitter, I would recommend making a scarf with light-colored worsted or chunky weight wool or wool-blend yarn and size 8 or larger needles. (Whatever you do, spare yourself the frustration of making a furry or novelty scarf as your first project!) Just use the scarf as a sampler as you learn stitches.
Once you get started, try a simple pattern. Always make a gauge swatch (so you don't wind up making a tank top that will fit you, your sister, and her boyfriend) and read through the pattern a time or two before you start.
You can do it! Just keep practicing, and you'll be flying along before you know it!