How will you use the mattress? If you intend to use the mattress for guests -- or even as your own temporary bed -- then you may prefer a double-height air mattress. These are roughly the same height as a normal bed, making them easier to get in and out of than a single-height mattress on the floor. If you plan to use the blow-up mattress mostly for camping, however, you might find a single-height mattress easier to fit into your tent. With a camping mattress or sleep pad, you should also pay attention to how long the mattress takes to inflate and deflate and how easy it is to carry.
How will you inflate your blow-up mattress? If your mattress is strictly for indoor use, then a pump that plugs directly into a wall outlet will be both quick and convenient. However, if you intend to take the mattress camping in areas where there's no electricity, you'll need some other means of inflating it. You could use a pump that's powered manually (such as a bicycle pump or a built-in foot pump), a battery-powered one, or one that plugs into your car's electric charger. Some mattresses don't come with a pump at all, so you'll need to buy one separately. In that case, make sure that the one you choose will work where you intend to use it, and also that it's compatible with the air valve on the mattress.
How big does the air bed need to be? Air mattresses aren't always as large as a comparable regular mattress and box spring -- although others are. Double-check the mattress measurements to make sure it's large enough for you to fit comfortably -- or that it's comfortable enough for two if you have a partner. This is especially important if you (or your partner) are taller than average. Check the mattress's weight capacity as well to make sure it can support your body weight (solo or combined).
Where will you store the air mattress? Consider the amount of room the air mattress will take up when it's deflated. Don't assume that you'll be able to fit the mattress back into its original box once you've unpacked and used it; without a vacuum pump, it may not be possible to squeeze every bit of air out of it for packing.