Riding with spurs is a little different and it takes a little getting used to. The smaller the spur, the easier it is to use. No, you would not be kicking your horse. Just remember that they are a reinforcement to your leg, just like a crop is, but it's less noticable. So you ask your horse to do something with your leg nicely (then harder) and if your horse doesn't listen you can ask them with your spur. The hardest thing to learn is how to ride without accidently jabbing them when you don't mean to. Also make sure that your leg is very still with your toes forward. I've seen people rub spur marks by letting their leg swing or by riding with their toes out. Your instructor should be able to help you out quite a bit getting used to them.
There are millions of different kinds of spurs and I would recommend the smallest and roundest ones to start off with, like a Prince of Wales, I think it's called. I also like Impulse spurs. They have a little rolling ball on the end that is pretty gentle but I find that horses respond very well to that. The original Impulse spurs are kind of long (which is hard to get used to) so I'd go with the shorter ones. Some spurs come with straps, some don't. Most are black but get whatever color matches your boots. Usually they all come in adult and childrens sizes. As for fitting the spurs Spastic Dove posted a great picture. The metal slides around the back of your foot. One side of the "U" shape will be longer then the other. That part goes on the outside of your foot. Make sure the spur points DOWN (if it has an angle to it). It should be wide enough to easily slide on but not so wide that they are flopping up and down. You can pull the metal sides apart or push the sides together to make them fit your foot better.
Putting the straps on the spur can be hard to figure out. Just mess with them until you can figure out how make them go through the holes and have it buckle on top of your foot with the extra leather pointing out (away from the horse).