Depending on the size, shape, nature and desired finish of your project - you can determine the most suitable abrasive to use based on a few basic characteristics. The two most common types of abrasives are bonded abrasives and coated abrasives. Bonded abrasives are the tougher abrasives that are generally used for bigger tasks such as grinding. While coated abrasives can be used for finer tasks like sanding. A large number of variations on these two types of abrasives exist through chemical and structural modifications that may be made to alter the cutting properties of the abrasive. You should carefully consider the texture or grain of your abrasive against the material you want to use for your project.
Harder abrasives might be a little too course for finer or softer materials, since it can remove too much of the material or leave unsightly scratch marks. These abrasives might get the job done quicker and last slightly longer due to the larger grain, but it might also degrade or destroy your project entirely if it is not used in the correct manner. Softer or finer abrasives, on the other hand, take longer to cut or blend your material and it will wear and become less effective a lot quicker. But finer abrasives allow for precision work and will tend to leave much finer scratch marks that might even seem invisible. Very fine abrasives can be used for finishing or polishing certain materials.
Aside from the actual texture of the abrasive - price and availability also need to be considered. Thought must be given to the desired task about using an appropriately hard abrasive. An excessively hard abrasive might waste money by destroying or wearing the material you are using it on, hence a cheaper and softer abrasive would suffice. But then again, if the abrasive is too fine or soft, it might also just waste your money. Because abrasion does not take place in a timely fashion and the abrasive is wasted and worn a lot faster.
Basically, you need to determine which grain or texture would get the best quality work done in the shortest amount of time at the lowest price for the material you need to use.