Expense
As with any purchase, think about how much you're willing to spend and how you want to use the product. More expensive albums aren't necessarily better; yet, if the paper is too flimsy, it won't be able to withstand the weight of your collection. Do you want to display your stamps in an unusual way, or do you prefer the arrangement to be laid out for you? It might be better to start out with a smaller, cheaper album as a practice run to see what kind of design aesthetic you prefer.
Beginner Albums
Stamp dealers offer albums for beginners that have pages with categories and marked areas to place specific stamps. Albums may also include facts about the stamps and countries they are from. The pages are fixed and can't be rearranged. These beginners' albums can be a good way to get the collection out of the shoebox and on to the pages, and also a motivation to continue collecting to fill in the spaces designated for any stamps you don't have.
Hinges and Mounts
Your preferred method of affixing stamps to pages plays a role in determining your album choice. Gluing or taping stamps to pages can damage them, so collectors use hinges or mounts. A hinge is a small piece of thin, translucent plastic with a small side to attach to the stamp and a side that sticks to the page. A mount is a clear plastic sleeve. Some collectors prefer mounts, as sticking anything to a stamp can be damaging; however, mounts are more expensive. Decide whether you prefer an album with blank pages, allowing for your own mounts or hinges, or an album in which the mounts are built into the pages.
Homemade
If, after exploring the store-bought options, you want to try out your own designs, you can create your own album. Purchase good-quality acid-free paper, either hole-punch it yourself or buy it prepunched, and use a three-ring binder. If you mount stamps on both sides of the pages, make sure you place clear plastic sheets of paper in between the pages, as the edges of the mounts can become tangled when the album is closed, tearing the stamps when you open the album.