I've been an amateur photographer for 10 years and a staff photographer for 1.5 years. In my experience, equipment is the second barrier on the journey to making great images. The photographer's "skill" or "eye" is her/his best asset. This comes through practice and review. Take lots of pictures every day if you possibly can. Take lots of pictures of the same subject. One of them will always be better than another one. Notice why. Look at them. You'll soon develop a feel or "eye".
Besides taking a lot of pictures and reviewing them frequently, one equipment-related thing helped me a lot: a prime lens. "Prime" just means that the focal length is fixed. It doesn't zoom. The main advantage to the beginning photographer is that now there is one less variable to control. (The side benefit is that prime lenses generally perform better in low light, and make clearer images than zoom lenses.)
Limiting variables is a huge help. Put your camera on "auto" or "P" mode for a while; its computer is smart enough to make good exposures without you adjusting it manually. Let it figure out exposure while you focus on composition and catching the moment. Reality is always changing; it demands your attention if you're going to catch the expression on someone's face.
For $1,000, you can find a nice lens/body combination. Consider starting on a cropped-sensor DSLR with a single prime lens.