Gauge is important because it has to do with fit. If your gauge is off, a garment you may intend to knit for a newborn might fit a one year old. I would hate to spend all that time knitting a sweater only to find it's too small in the end. You will need more stitches with a lighter weight yarn such as fingering, sport, or baby sport yarn and less with yarns such as bulky and super bulky. You'll have to adjust your pattern accordingly. Not all patterns are suited for certain weights.
I have a similar book called Teach Yourself Visually: Knitting Design by Sharon Turner. It's great, but there's something you should know about those books. Mine tells you exact sizes and how many stitches you should cast on, which is great. It's a step by step guide. However,the sizes are misleading. Technically, if you have a certain size head measurement, it should fit. Practically, it doesn't. The hat slips around on your head and pulls up off your ears where it's supposed to be. Experience has shown me that I have to make those hats about one or two inches smaller width-wise than what the expert tells me I should in order for it to fit right. This is why you have to play with these patterns a little. Hey, you can always frog it and start over.
Your yarn depends on what you want. A lighter weight yarn like sport yarn might be okay if you're working in an office. If it's summer time, you have to take into account air conditioning. A question to ask yourself is: are you going to wear the garment for warmth or just fashion? If it's just for fashion, you might use weights such as fingering, sport weight for lacy things such as a vest to wear over a blouse where modesty isn't an issue. You don't want your bra showing through.
It also depends on your climate. If you live in warmer ones, cotton yarn might be an option. Keep in mind that cotton doesn't stretch as much. Again, you'd have to adjust your cast on stitches accordingly.
Outdoor garments are another story. Here in Wisconsin, it's best to have two sets of mittens, hats, scarves, and sweaters for warmth under snowmobile and down jackets. One is knit in a sport weight yarn and is good for those 30 or 40 some degree days like early fall or spring. Anything heavier would be too warm. December, January the temps get down to 30 below zero and you'll need a set made from worsted or bulky weight yarn. A large size needle is okay for the bulky and super bulky. For the other weights, you want a smaller needle like a 4 or 5 to make the knit denser and warmer. I hope this makes sense to you.