Others have already suggested places to take sewing classes, so I can't help much more there.
As for beginner projects, maybe a simple drawstring bag, pajamas, or a simple stuffed animal? The simple skirt is also a good suggestion. Pillows are probably another good beginner project. You could make a custom pillow (or pillowcase) in your favorite colors.
And for crafts, I'm not sure what to suggest, really. maybe take some little bottles, and decorate them with wire/beads, and paint? I have no idea about that, sorry. A lot of people seem to like making polymer clay (Sculpey, Fimo) crafts and sculptures. I, personally, like to make stuffed animals (and we're back to the sewing bit there).
Oh, and when sewing with a machine, try to go easy on the speed at first, light on the pedal. I think most if not all machines have a dial you can hold onto a bit to help slow down the speed, and there's the option to hand-turn the wheel in tight/difficult places. When I first started sewing I had to hold on to the wheel a lot. ^^;
And ALWAYS pay attention while sewing on a machine! Watch your hands, because now I've had TWO friends who have sewn through their fingers while distracted (one even happened while I was there...). But as long as you're careful, you should have no problems.
Also, make sure your needle is right for the job. There are different kinds of needles for different fabrics. And make sure you don't sew with a bent/damaged needle, always keep extras on hand.