Bikes should have the saddle height set so that the leg muscles can drive the pedals efficiently. As a general rule, when you are sitting on the saddle of the bike with the pedal furthest away from you, your leg should have a slight bend at the knee, or your leg should be straight with your heel on the pedal. If the saddle is set at the correct height, you may not be able to touch the floor when you are seated, however, when stationary, you should be standing over the frame and not poised on the saddle.
Your upper body position on the bike will largely be determined by the style of bike you chose. A hybrid style commuting bike will have quite an upright position putting little pressure on the neck and lower back, whereas a road (racing style) bike will have a much more aggressive position for getting up to speed. You must factor in any injury history you may have and be realistic about what your body can cope with.
You can get some good online resources to guide you on fitting or you can visit a bicycle retailer and take advice, but whatever you do, get properly fitted up if you want to get the most out of owning a bike.