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Upright
Upright vacuums have the strongest suction and the advantage of standing upright in a one-piece unit that won't tip over. They often come with attachments. They can be quite heavy. Be sure the head doesn't have brush rollers.
Stick
Stick vacuums are streamlined versions of upright vacuums. They are upright but skinnier and lighter, making them well-suited for smaller spaces. They are usually only designed for hard floors, so if you need a multi-floor vacuum, this isn't your best bet. They are generally cordless.
Robotic
Robotic vacuums work on their own and have sensors to work around obstacles such as walls and stairs. They can be scheduled to run, and some people like using them daily,best hardwood floor vacuum consumer reports especially in households with pets. Be aware their dust capacity isn't as great as other types. Some models can get stuck or may have limited battery life.
Other considerations
Pets: If you have pets, select a vacuum with powerful suction to make up for the lack of bristles to pick up pet hair.
Capacity: For larger floors and homes, consider a vacuum with greater canister size to collect dust and debris without having to empty the unit frequently. Robotic vacuums have the smallest canister size.
Cordless: Cordless models operate on rechargeable battery power and are highly convenient. They also tend to be quieter than models that have to stay plugged in. Be aware they don't provide as much suction and have limited running time.