Hi Jeanne, the order of strokes is extremely important in Chinese. Not only it makes the characters look good, it also determines the number of strokes of a character. This will facilitate you to search for the character in a dictionary. In addition, if you don't follow the order of strokes correctly, then you will not be able to learn Chinese calligraphy, which is an ancient writing art.
In general, Chinese characters are written from top to bottom and left to right. Traditionally, Chinese books and newspapers are read vertically from top to bottom and right to left. As compared to westerner, Chinese tend to read books from the back to the front. However, nowadays many Chinese books are also published in western style which is horizontal and from left to right.