Fuel type
Home pizza ovens run on either gas, charcoal or wood. Propane and natural gas pizza ovens can be connected quickly, ignite instantaneously and heat up in just a few minutes. They also burn clean, with less smoke and little mess to clean up.
Wood and charcoal ovens, in contrast, need to be loaded (and sometimes reloaded) and take longer to heat up; also, an even temperature is trickier to maintain. They also make a bigger mess, leaving behind ash and soot.
And though you may assume wood-fired pizza ovens would impart a smoky flavor, the pies are not in the oven long enough to absorb much of that wood flavor.
Size and portability
If you have a dedicated space for your oven, a larger, heavier model should work. If you'll be looking to store it away between uses or move it around regularly, a more portable oven is a better choice.
Accessories
One accessory you'll definitely need for your new pizza oven is a pizza peel. This unique paddle-shaped tool allows you to safely slide a pizza in and out and rotate it for even cooking. Remember, these ovens get as hot as 950 degrees so you don't want to take any chances with a shaky spatula or tiny tongs.
The other accessory you'll likely want to invest in is a cover, especially if you plan to leave it out in the elements between uses. Some pizza ovens come with a custom cover, but many don't.