
SEBO
AIRBELT E3 Premium
Ultra-durable, 10-year warranty, but expensive with short cord.

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I think that's what I've got as well - mine's the 'TruePet Lift-Away' but I think it's the same general model. The only issue after 5.5 years is that the stick doesn't click into the base very well anymore.
I have a Shark Liftaway True Pet and love it. Did a ton of research before buying for something that can handle pet hair, go under furniture, easier to do stairs etc. It checks all of your boxes and is currently $355. https://a.co/d/0ayb32oD
If you’re okay with going a little over budget I have a 13 year old Shark Rotator and love it https://amzn.to/4o58DIU I actually tried out the Dyson a few years back and decided to return it and stick with my Shark. They have an older model on Amazon for 299 https://amzn.to/46UL5Ab it’s a powerful vacuum that works well with cat hair, carpet and hard floor surfaces. It’s lift away design helps get under furniture which helps tackling cat hair.
Shark NV752. Only thing I bought on Black Friday. I like it a lot.
I’ve had the Shark TruePet since 2020, and it’s still holding up great. I do have to cut long hair out of the rollers every few months (three daughters in the house), but it’s been solid on both carpet and hardwood. I think I paid around $250 for it at the time. That said, I’m actually shopping again because my youngest has allergies, and I was told that a bagged vacuum with HEPA filtration can make a big difference. Those three things together (corded + bagged + HEPA) do push the price up, but I’ve seen a couple of Hoover models that land closer to your budget. If you’re still looking, definitely check out the [Vacuum comparison sheet](https://www.reddit.com/user/lacking_foyer48/comments/1lj76h3/vacuum_cleaners_compared_comprehensive_datasheet/) that I saw on another subreddit. It compares all the models and brands side by side. I’m using it right now to shop, and it really helps narrow things down no matter what your priorities are.
I actually clean houses for a living and my girl and I use the shark pro true pet rotator. We especially like the fact it has a light on the handle/wand. We've gone through maybe 4 different shark brands and this one is the best so far. Many of our clients have Shark brands so I've used a bunch of different types. We clean a minimum of 2 houses a day for each day of the work week. By and large, they each last roughly 2 years before the heads get "floppy" or the clips that hold the wand in begin to fail.
With 2 dogs and a cat I think a cordless won't do as good a job as one with a cord. I have 3 small dogs and my cordless needs to be dumped many times when doing the house. I like my shark rotator...I think it's called a "Tru pet" or something like that.

SEBO
AIRBELT E3 Premium
Ultra-durable, 10-year warranty, but expensive with short cord.

Numatic International
Henry Canister Series
Budget king, super durable, but heavy and poor on carpets.

SEBO
AIRBELT D4 Premium
Durable, powerful, long cord, but heavy and pricey.

SEBO
FELIX Premium
Durable, powerful, good for allergies, but heavy with awkward attachments.

Miele
Classic C1 Cat & Dog PowerLine
Durable, powerful, quiet, but very expensive, short cord.

Ranked #1
SEBO - AIRBELT E3 Premium

Ranked #1
SEBO - AIRBELT E3 Premium

Ranked #1
SEBO - AIRBELT E3 Premium

Ranked #1
SEBO - AIRBELT E3 Premium

Ranked #1
Numatic International - Henry Canister Series

Ranked #1
Dyson - V15 Detect Series