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

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I have a Bissell Power Force compact from Walmart. It's about $60. I've had it for about 3 years and it's still working great! And I have a car that sheds like crazy!
Yeah that's a really tight budget which limits your options. I'd go for either a bissell powerforce bagged from walmart if you want the most powerful and best air filtration. You do have to buy disposable bags which collect the dirt, but they are easy to find and pretty cheap. And since it uses a bag, you don't have to clean filters and it retains dust way better than bagless models in that price range. Otherwise the bissell powerforce compact is a smaller and slightly cheaper options. It's not as good and you have to clean the filter really regularly on it, but it is more compact which might appeal to you.
It really depends on expectations and needs. Realistically, most vacuums on the market will do some jobs just fine. What makes the difference is how well it'll do the job, how many kinds of jobs can it do well, how much work it takes to keep it working properly, and how long it'll last. Plus higher end machines tend to be quieter and more refined in every way. But on a budget, foregoing refinement is an acceptable compromise. It's about managing expectations. For under $100 you'll be looking at single purpose vacuums. Uprights in that price bracket are really only good for carpets and not hard floors, plus they have pretty lacklustre hoses and tools for corners and furniture vacuuming. If you need good hard floor vacuuming performance, you might need to consider a second vacuum. Also upright vacuums in this price range tend to have poor filtration and aren't recommended if you have allergies. Basic uprights also require the brush drive belt replaced every 6 to 12 months, not a hard job or an expensive part but it's maintainence. Canister style vacuums in that price range are acceptable on hard floors and usually have at least one or two small attachments for other jobs. But they lack a spinning brush making them only suitable for removing loose debris from carpet. Filtration is again pretty basic too. Stick style vacuums in that price range are....good at being lightweight I suppose. Not very good for actual cleaning. In your case if carpet is the main consideration, the bissell powerforce bagged is a decent choice. It's avaliable from walmart exclusively and is around $75. The bags and belts are both bissell style 7 and are easy to get. It's important you get the bagged version though. It has acceptable filtration and the bag means you don't need to regularly clean any filters, just throw the bag out when full and change that belt now and then. The bagless versions I would absolutely avoid, the filtration is really poor causing a lot of dust to be blown back into the air, and the filters need cleaning very regularly which can be a hassle. The poweforce bagged is pretty much the only sub-$100 bagged upright avaliable. Only other downsides are again the very basic attachments, basic everything really, and it won't really vacuum hard floors (it has a hard floor setting but the brush does not turn off, so it really just fires crumbs clear across the room on bare floors).
I have a dyson stick that is many many years old. I love it and use it daily. However, it is not sufficient for carpet. It gets the little bits in between cleans, but if I do a dyson pass and follow up immediately with my cheapo bissel standup wall plug vacuum, that thing picks up sooooo much. Just an insight from someone that's not going to tell you theres only two vacuum options you should consider or else.
You'll want something with good suction and a beater bar-especially if you have long hair or pets. Downside- with cheaper you'll need to go slower and more frequently. Don't fall for the hype of those carpet powders- they're just baking soda and perfume and will actually funky up a bit because your vacuum won't pull them up as well as you think. Also very terrible if you or any guests have respiratory concerns, like asthma. Bissell Upright Powerforce is a good cheap option. Its not perfect, but they do have bigger cannisters than the handheld sticks. They usually run about $50-70 for the standard and helix models. Again, you'll still need to take your time and run back and forth a few more times than some of the fancier pricier models, but they get the job done if its just daily dust collection, and not super deep clean intended.
Bissel Powerforce, it’s the best vacuum I own (I also have extremely pricey useless Dyson and a slightly better Samsung). Nothing cleans as well as the Bissel. It was like … 120? And it’s light, so light it feels junky but it works so well
Don't waste money or overpay for a vacuum. By the bags, bistil upright at Walmart or online. Those things work great are easy to repair and work.Relatively good on bare floors. I think they're like sixty dollars or so.
End of reviews

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