I have the same one and I quite like it, so I can say that it is definitely a great machine. It should be safe to buy from Amazon because since Sears is not really a thing anymore, the company that manages and produces the Kenmore vacuum cleaner line has been using retailers like Amazon to sell their units.
You could also consider the Kenmore Elite upright which is about the same thing, just with the main differences being a more powerful suction motor, a fancier brush roll design, and a 35 foot cord instead of a 30 foot cord.
Kenmore BU1017 is cheaper at Amazon at $250 after coupon. From what I understand, it is the exact same as the Kenmore 31150 except for a different color.
https://www.amazon.com/Kenmore-Lightweight-Handi-Mate-Telescoping-5-Position/dp/B08M2TWTQX
The Hoover WindTunnel T-Series Bagged is a decent vacuum cleaner. It is a recently discontinued model, so while you can still purchase it, the price has inflated from its normal $99 to $150 (it went on sale frequently) all the way to $200, so I personally do not think it is as good of a deal as it used to be. You get $99 build quality for $200, being my main issue with it. On the other hand, the T-Series is effective at cleaning carpet, fairly lightweight, and has nice HEPA bags.
If you are interested in a budget upright, I would direct you towards the Kenmore BU1017, which is typically around $300 and currently on sale for only a little more expensive than the Hoover. Not only is the build quality better than the Hoover by a lot, you also get better features such as a dirt sensor, sealed HEPA exhaust filtration, LED headlights, no belt that needs to be changed, a brush shutoff on the handle instead of a mechanical one, rubberized wheels for hard floors, a lot more suction and airflow, and so forth. The leap in quality and features used to make sense when the Hoover was cheaper, but now I rarely suggest the Hoover because the Kenmore uprights are undoubtedly better. The main downsides of the Kenmore BU1017 are that it is heavier than the Hoover and that the on-board hose, while short like the Hoover's, is a little more awkward to use due to being mounted quite high on the back of the unit. Unfortunately, Kenmore no longer sells an upright extension hose, though maybe they will start again if we harass them enough.
The Kenmore 200 and 400 Series canisters are a decent option, especially since you can get a 200 Series for as little as $199 at Walmart. A canister is nice if you want versatility with attachments for cleaning things like furniture and cars, both tasks I find annoying with the Hoover and Kenmore uprights I just mentioned. Plus, attachments like a miniature power nozzle, dedicated upholstery tool, dedicated dusting brush, and so forth can be added. Kenmore has used the same fitting for decades, so many different attachments that have been made over the years will work. The main thing to note when looking at all the 200 and 400 Series options is the attachments. Most of them come with power nozzles, but their little attachments and wands differ. The 200 Series models also lack the variable motor speed, power switch on the handle, and bag check indicator that the 400 Series models have. In terms of cleaning performance and radius, they are all the same with the same motors, same power nozzle (for ones that have it), same hoses, same cord reels, and so forth. Of course, being a $200 canister, they are not perfect. The main issue I have with them is that they use a bag dock design straight out of the 1990s that relies on a foam seal on the bag dock itself instead of a modern design with rubber seals in the bags like what can be found on the uprights I mentioned, so the Kenmore canisters heavily benefit from using the genuine HEPA bags that have better filter material and thicker collars than the non-genuine options. With that said, the worst thing you may have to do is rinse the pre-motor filter in the bin every so often, hence why they have never bothered to update the design. They did bother to seal the exhaust system, so all the Kenmore canisters are sealed HEPA systems now, so do not let anybody tell you otherwise.
The Numatic James JPV180 is certainly an excellent vacuum cleaner. It would be better than a Kenmore canister in many ways, although it lacks a power nozzle. With thick and long pet hair on carpet, you would want something with a spinning brush, and that is something that would not be able to be achieved for under $300 with James, who just comes with a combination hard floor and carpet tool without a spinning brush. There are spinning brush options such as turbo tools from brands like Wessel-Werk that are the best of the best, although they still will be much more maintenance than an electric brush, not work quite as well on thicker carpets, and be more of a hassle in general.
If you want something more premium with a power nozzle, I would suggest getting one of the cheaper options listed and saving up for something such as a Miele Classic C1 Cat & Dog, Sebo K3, and onward. Something like the Kenmore uprights or canisters should easily last you five years or more if you are interesting in putting some money aside for something fancier. Hey, treat it well and the Hoover should even give you a solid lifespan.
The Kenmore Intuition is a more budget oriented model that seems to be outsourced to a company that makes swiveling uprights for a lot of different companies. One major place where companies that make these affordable machines slash the build quality is in the hoses, so the material they use in the Kenmore Intuitions, like with units from other brands like Shark and certain Hoovers, is fairly weak. They are a decent deal when they go on sale, but they are more cheaply built than they should be.
With that said, the Kenmore brand still offers some of the better affordable vacuum cleaners out there, and basically the only budget canisters with power nozzles. They are hit or miss. Their more expensive stuff is actually pretty good and I have definitely asked for follow ups a lot of the times I have suggested them and buyers generally like them, especially their one CrossOver bagless upright.
If you are looking for an affordable bagged upright, I would go with the Kenmore 31140. It has more features than the Hoovers such as a separate brush roll motor with an on/off switch on the handle, a lifetime belt, sealed exhaust filtration, and so forth. It is more expensive than the Hoovers, but worth the money because the build quality is that much better. The BU1017 is about the same unit, just loaded with more features such as a dirt sensor, one more height setting, a longer cord, a fancy geared brush roll, a slightly more powerful motor, dual headlights, and that is about it. It's not much more expensive than the stripped 31140, so definitely consider it too. The downsides to these units are that they are somewhat heavy and the attachment hoses are short, but they clean really well and come with extender wands and long crevice tools. They were designed by Panasonic and are made in-house by the company that licenses the Kenmore name; a company that has manufactured Kenmore vacuum cleaners and parts for a long time.
If the Kenmore uprights are too expensive or you are worried they may be too heavy, the Hoovers are decent. I have found that a lot of the Hoovers have reduced in build quality in the last five or so years, but the bagged ones tend to be more consistent. They are lighter than the Kenmores and cheaper, so they have that going for them. Plus, they do clean well and bags are cheap and easy to find.