A good cheese basket has variety, in textures, flavors, and uses. While a theme to the cheese basket is generally useful for keeping you from having many random cheeses, such as a wine and cheese basket, a good variety keeps it interesting. Find out what cheeses the receiver loves and be sure to focus on those, while trying to introduce new cheese delights.
As mentioned above, a theme for the cheese basket is a good idea. You will also not want any one flavor of cheese to clash dramatically with another. Make sure it each cheese complements the whole basket in some way, rather than throwing a bunch of random cheese together. This will make the basket a more thoughtful gift, rather than just a basket filled with assorted cheese.
There are some cheeses that simply do not last well in the open or in gift form. They may melt or start to turn sour if they are not immediately taken care of. It is best if the cheeses you choose when designing a basket have a good life unrefrigerated and can handle a little heat before spoiling. Cheddars especially are known for their longevity in a basket.
Many cheeses have very strong flavors, and due to their composition, can bleed that flavor into other nearby cheeses. In some cases this is fine, in others it can lead to an less than savory combination. Use tasteful separation pieces, like other foods such as crackers or fruits, or wax paper or other materials. This will ensure that the cheeses are kept fresh and uncontaminated in flavor.
5) Include Other Tasteful Cheese Related Gifts
A cheese basket will be consumed eventually, and the remembrance of it will fade without something more lasting. So why not include a more permanent, tasteful cheese related accessory. Items like cheese knives, graters, presses, and curdling supplies are great examples of these gift idea. Make sure to include the item into the basket in a fun and design minded way. They are sure to remember the cheese basket much more clearly with fun additions like these.