It looks like I can find a 250gb sub $30 but I don’t understand the differences .
Would this one be good and max out speeds? https://www.amazon.com/JOIOT-Portable-External-Ultra-Light-Windows/dp/B08CV5GTMS/ref=sr_1_9?crid=ICYM4OGIUJDT&dib=eyJ2IjoiMSJ9.Aop0mVxQNamtYQ6Nfht46AHGYIkEA4fK-8_oBNELtGiVicxVRL3VEEvoO7-tcAB-ZQNmKCYYI9ktCtJTR9858khqiOr7zvKr6dHkzr9HDCYBYpkCRIbhp_4NByIfoJ0UfIoPFxeE1jO4m6Vpk9B8qwBOQxpJRD0Cy8Lb95XsUe1G-7FwmFEd703PqYIdU15xeiIbkmzywD1MBcEnW_Cz6oNwKdcbMHdMUenh8bexNA9Dsm3yxaKZfRF1oFcpaTqX0RaDaVwqsvUBu569C2r7XNqyQpUeAWle4CiRhUQTu2o.u1N90mfjXbg7blLKGp7rDv2mcvstdIP0R0OSoc3NIDs&dib_tag=se&keywords=External%2Bssd&qid=1710167797&refinements=p_n_feature_twelve_browse-bin%3A41942641011&rnid=41941853011&s=pc&sprefix=external%2Bssd%2Caps%2C82&sr=1-9&th=1
What do you intend to use that SSD for?
A Raspberry Pi doesn't necessarily need that type of SSD drive and you certainly don't need one for home assistant.
At minimum you need a Micro SSD card like one of these:
https://www.amazon.com/s?k=micro+ssd+card&ref=nb_sb_ss_ts-doa-p_2_9
A 32 GB or bigger card is recommended.
One thing you may consider is getting an A2 rated CF card. Those are much better for application support and are only a couple of bucks more than the standard cards. See Understanding the Naming Conventions and Labels of SD and microSD Cards - Kingston Technology for an explanation.
I have often read that SD cards are not ideal when you have a lot of read/write operations. The level to which that is still correct nowadays, I am not sure, given likely advancements in SD cards, but I have always chosen to purchase an SSD drive for each of my RPi4's. I have purchased Samsung Evo's each time, plus a UGreen enclosure, though the enclosure is not powered, which I believe is also a common recommendation. I haven't had any issues with these options, though I'm not exactly stretching their likely capabilities, which I expect would also be the case running HA.
Another thing you may want to consider, particularly if you are running a Zigbee stick for HA, is to purchase a few short USB extension cables. Having the SSD too close to the Zigbee stick can impact the signal quality I believe. Having an extension cable for both the SSD and Zigbee stick would be ideal.
I'll just add, brand name, reliable source to this.
There's a bunch of crap floating around out there. 
I run SATA SSDs on both of my PI4s. One of the key things is the enclosure. This page -- Best Working SSD / Storage Adapters - Raspberry Pi 4 / 400 helped me pick the uGreen SATA -- https://www.amazon.com/dp/B07NPG5H83
I wouldn't use the term need, but it's definitely not advisable to run HA on a microSD card because of this:
HA is constantly writing to the internal DB so you'll wear out an SD card pretty quick.
I'm prepared with backups, but so far (2 years now), I've been running my RPi4 with this SanDisk High Endurance Micro SD card and I've not experienced any issues or slow performance. I have had a 128 GB version recording contstantly in my camera at the front for 4 years without fail.
I became paranoid about my Pi 4 SD card 'wearing out' and cloned it to a SSD. Fairly sure I used a Samsung.
I'm pretty hopeless with the Pi and blindly copy/paste code to get things working from tutorials. I've no backup so at some point will be in trouble. I installed some AFP utility where I can browse the Pi from my Mac so perhaps I could backup bits of it that way...
I'm not saying it isn't possible...just typically not advisable.
I've not seen anyone say they were using a High Endurance SD when they had a failure. Every account I've read, they name some cheap SD card or one that was never designed for being constantly written to. I'm not thinking this thing is going to last forever, so I'll post an update when it eventually dies.
Doesn't matter what you use, you had better have a backup plan. Nice that HA automatic backups to Google Drive are free.
I prefer the samsung external ssd drives for things like this ie the t5 or t7.
Also to OneDrive: Addon - OneDrive Backup - Share your Projects! - Home Assistant Community
I backup my HA to OneDrive because I have 15G there and I never otherwise use it. My GDrive is full of photos.
Basically any SSD is more than “fast enough” to run home assistant on a raspberry pi for the vast majority of use cases. It’s unlikely you’re doing anything with home assistant that needs to “max out” the read/write speeds offered by an SSD.
As others have pointed out, what you really want to consider is reliability of the flash storage you’re using with the raspberry pi.
Some people avoid SD cards for that reason. Or use high endurance SD cards.
But if you use a no-name SSD like the one linked to, you might still end up with a reliability problem because they use crap components.
Personally, I’d probably go with a reliable, high-endurance SD card in this scenario.
I really like the reboot speed of a SATA SSD compared to an SD card.
I originally switched to an SSD because of the MongoDB used by the UniFI controller. I would never go back to an SD card.
If you have an rpi5 the nVME bases are cool.
I have simply used a USB3 to SATA adapter cable, with a Samsung SATA 2.5" SSD to boot a RPi 4 running HAOS for the past few years. It has worked perfectly.
USB to SATA cable
https://www.amazon.com/gp/product/B00XLAZODE?th=1
Samsung SATA drive (I think mine is actually an older model)
https://www.amazon.com/Samsung-250GB-Internal-Solid-MZ-77E250/dp/B08T1TWQS9?th=1
Since all power for the SATA SSD drive is provided by the USB3 port on the RPi, it is very important to have a very decent, high quality, high output power power supply for the RPi 4. Don't skimp on this or else things will not run stably.
Lately, I have been messing around with a RPi 5 8GB, with a Geekworm X1003 NVME Hat, plus a Samsung 2242 NVME drive. This all fits neatly within the official RPi 5 case. Again, use the official RPi 5 Power Supply.
Geekworm NVME Hat
Samsung 2242 SSD
https://www.amazon.com/gp/product/B0BPF4KM68
That's where an A2-rated SD card helps. It means the card is faster on the small reads and writes that applications tend to do. I got a Samsung 128 gb SD card: it's only $16. https://www.amazon.com/gp/product/B09B1JFY24/ref=ppx_yo_dt_b_search_asin_title?ie=UTF8&th=1
I went with a $10 Samsung m.2 128gb and a $10 orico enclosure. $20 and it’s wayyyy faster and more reliable than a micro sd. I don’t even know why the micro sd is reccomended .
If I could do it over, I’d buy this for $25 https://www.amazon.com/SSK-128G-Portable-External-Gen2（6Gbps）/dp/B09MTH3B69/ref=sr_1_3?dib=eyJ2IjoiMSJ9.ycjAPSFe7sV0IOJXYCOQFEP7UbIsHUQzpNGCyQmOmYLtpUSPHMCKOQoUa-PNzx4ARo7hgOOLmqBEsLgK06aSDGNkQ26Df81r8ikxrM1hY4Xbi8_DFuXAoW2V53JYwEGqGfOtCOjNC_pwkddwveAeuLUeOn5guik_CD1FZ39TvPcShfMFZDD-JohsKkk59oHttE9iThJAKDBSRBhUawaHNPR2737swTw-lffJV0Io78s.0xTWLdgKJzLWhIZFTEFT_lVegIKNvQnxFPCDtS_K01M&dib_tag=se&keywords=128%2Bexternal%2Bssd&qid=1711806394&sr=8-3&th=1
But I do think Samsung is more reputable so maybe not
