which is the best external ssd for running macOS, please?

'Best' is subjective.

'Fastest' would be a Thunderbolt-3 drive, and 'highest quality' is arguably an Envoy Pro by Otherworld Computing.

However Thunderbolt-3 drives are overkill for typical users.

'Best Value' would be a USB-C drive. A generic Sandisk Extreme or Samsung T7 should get the job done just fine for a third the price of an Envoy.

Depending on how much you want to spend a Thunderbolt drive can be 4x the speed of a USB drive. I have both and an NVME drive in a TB enclosure is the fastest. I use WD NVME drives in various enclosures that match my internal SSD speeds.

To be perfectly honest there is no "best" in anything, there is no best SSD, car, house, job, dog, nothing. What there are is choices as everyone's needs are different. If you want the fastest and most durable then I'd say get the OWC Envoy Pro EX Thunderbolt 3. However if you don't need that type of performance then I'd recommend OWC Mercury On The Go Pro & OWC On the Pro Go Power Adapter which is a bit slower and more economical. You have lots of choices these days, the reason I recommend OWC is because they specialize in Macs, everything they sell works, their products have very competitive pricing and they offer great service.

I have had Lacie products and did not have great service from them so I don't happen to like them, however that is just me. From what I read several others like them, that's great though. The good news is you have choices and you need to find a product that most closely suites your needs.

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I like LaCie SSDs sold from Apple. For specific links and setup instructions, please see: How to Setup and Use an External SSD as y… - Apple Community.

Jack

You are wise to install the much faster external SSD to install the OS on. As to which brand to use, you will no doubt get many, many recommendations. Most any of them should serve you just fine. I have use LaCie disks and have been completely satisfied with them.

on the OWC (MacSales.com) external SSD.