Ranging from smallest to largest, what is the correct order of structure within a cell? choromosomes, DNA, gene or base pair?
The base pair is the smallest of these structures. The term "base pair" usually doesn't even include the deoxyribose sugar or the phosphate group that compose the backbone of the DNA; it just refers to the complimentary nitrogenous bases that form the "rungs" of the DNA "ladder". Cytosine pairs with thymine, and guanine pairs with adenine. A base pair is either of these two molecules, evaluated when they are in a position to be linked by hydrogen bonds. This structure is composed of only a few dozen atoms.
The next largest structure is DNA. The term "DNA" is being used a bit loosely here; it can refer to a single phosphate-deoxyribose-nitrogenous base group, or to the double-helix form that is normally found in the nucleus, or to the entire strand of DNA. It helps to have these sort of things specified. For the purposes of this model, I'm going to assume that we're talking about double-helix DNA, in which case we could take the base pairs from the first example and tack a deoxyribose and a phosphate onto each of them, in order to illustrate how much bigger they are.
The next largest is a gene. The exact size of a gene is difficult to determine because so many genes interact with a variety of DNA surrounding the specific protein-coding region; however a good number would be something like 12000. This would make the gene 12000 times larger than the DNA considered in the previous step.
Finally, a chromosome would be the largest structure. A chromosome consist of hundreds or thousands of genes, and potentially millions of base pairs.