There are two major choices to be made in picking an album: style and size. Other minor considerations such as cover materials, cost , color, decoration, etc. have more to do with personal preference than function
As for size, the most common sizes and the ones which have the largest variety of paper available (patterned and solid cardstock) are 8 1/2 by 11 and 12x12. These are the two that most scrap bookers use for their family albums. Other sizes from larger to smaller to micro mini are sometimes choices for gift albums, specialty albums, or to scrap things like newspaper articles. The 8 1/2 by 11 size will generally accommodate 4-6 pictures and require less decoration of the spaces in-between. The 12x12 size allows for more creativity, space for journaling and additional pictures: 6-8, and sometimes more depending on how they are cropped. The size part is usually the easier of the two major decisions to make. If you are not photographing everything in sight, perhaps the 8 1/2x11 will suit you well. If on the other hand, once you start scrapping, you take many many pictures of each event, (this is me) you will really need the 12x12.
More of a decision is the style of book you want. And opinions vary widely on this. There are strap hinge, with slip on or top loading page protectors, post bound, spiral bound, and 3 ring binders. Let’s go over each one:
Strap hinge: This style book is the one used by Creative Memories. Creative Memories has been at the forefront of the increase in interest in scrapbooking. It’s a little difficult to describe without having one in your hands, but basically the book has a staple type projection on the edge of the pages and these are bound into the album with a plastic strap. They require a certain amount of effort to undo and rearrange when adding pages, but, when spread out the side by side, pages are very close together and make an appealing presentation. The pages in these albums also have a “jeeping” on the right and left margins of the pages, which add stability. The original intent was that these pages themselves be the background for your layouts. It requires some forethought when designing your pages. If you work front and back on the page, you cannot rearrange your book if you find something later that you want to fit in. But many people use them for wedding albums. The most often used of these style books are made by Creative Memories (purchased from a consultant) and Westrim, available on-line and also in hobby, craft, and LSS stores. The original page protectors for these books were slip on, but they now have top loaders available, which allow you to use different back ground paper and rearrange your pages. One draw-back: the scrapping space on these pages is not true 12x12 or 8 1/2x11 and requires trimming of all papers used for wallpapering (the term used to describe covering the white page with patterned or colored paper).
Next are post bound books. There are any number of manufacturers who provide these from Daylee (high end) to Generations by Hazel and Pioneer (which are available in lots of places including some supermarkets and Drug Stores). These books have screw in posts, which can be added to with post extenders as your book grows, and are easy to take apart and reassemble when you add more pages. They come with white or black pages inside a page protector (top loading), and you can use their paper or any other paper of your choice. It is very easy to rearrange your book by merely taking your finished pages and moving them around between protectors. It is the page protector and not the paper which is bound into the book.
A third type of book is a spiral bound book. These are not commonly used except for a gift or specialty album where you know exactly the order in which you are going to work. The pages cannot be arranged once completed.
Three ring binders are easy to use and offer the greatest ease in rearranging pages. D-rings are better at keeping pages flat, but O rings make it easier to turn the pages. Completed pages are placed in top loading page protectors. And the rings hold the page protectors. While easy to use and affordable, these books do leave a gap between the pages of a two page layout which may or may not concern you.
One other hint, all albums, page protectors and papers are not all “true to size”, even though they may be labeled 12x12 or 8 1/2x11. This seems to be more of a problem with 12x12. So beware that you may have to trim some papers to fit in certain page protectors.
Hope this helps. Choosing covers of leather, cloth, vinyl, or tapestry and the color, design and cost of each are a matter of taste and add to the fun of scrapbooking. Some folks want all of their albums to be identical, some have the spines embossed with names or dates or events (this can be done on the cover also), others, like me, want to experiment with all different colors and textures. So have fun.
I may not have covered everything here, but hope I have given you a general idea which will allow you to decide on an album. And remember nothing is written in stone. If you start out with one size and style and decide it’s not for you, you can change with your next album.