install external ssd or internal ssd on mac mini late 2014

Another option would be adding an OWC NVMe SSD to the mini (link below). The beauty of this option is that the only thing you need to do to the mini, is pop open the back cover and antenna plate. And with the antenna plate, you don’t even need to disconnect the antenna wire connection, just slide the plate off to the side. Installing the NVMe SSD is a snap and OWC has videos showing the process. Takes all of five minutes.

https://eshop.macsales.com/item/OWC/S3DAPT4MM05K/

So, you’ll still have your internal HD for storage/backup, you’ll be booting from the NVMe SSD which is incredibly fast, and with the internal Apple HD you’ll still have the option of booting from an external SSD just in case. That’s the system I have with my 2014 Mac min and I couldn’t be happier.

FWIW, the external SSD approach is very easy and zero risk compared to ripping your Mac apart.

The 2014 Mini has USB3 ports, while not the latest and greatest, will still make the system seem like a speed demon with an external SSD as compared to the sloth slow HDD internal.

As far as internal drive failure issues with external bootable drives, that is really only an issue with M1 and M2 Macs. I was running a late 2013 27" iMac that had a failed internal HDD for a few years on an external SSD until I got up the nerve to open it up and install it inside.

Plus, getting the fast current generation of external SSD drives, when you get a new Mini it will work great with it.

The best option, is to consider replacing the 2014 with a new Silicon Mac mini.

There's a refurbished M1 for $470 see > Refurbished Mac - Mac mini - Apple

Or consider one of the brand new M2's for $600 see > Mac mini - Apple

The second for speed, is to replace the old 2014 Mac mini's HDD with an SSD.

Which requires an SSD and the skill to completely disassembly the Mac mini.

Google > iFixit Mac Mini 2014 and check out the Hard Drive section.

The third option is not a bad one, but can be problematic if the internal HDD fails.

see > Use an external SSD as your startup disk … - Apple Community

I would recommend that you look at the install videos for your specific Mac mini on OWC’s website to see if the internal drive replacement is something you are capable of doing.

if you cannot, or if you don't want to pay a professional to do it for you, then the external SSD is your other option.

to implement that, please see Use an external SSD as your startup disk with your iMac or Mac mini - User Tip

just about any manufacturer's external SSDs will work. but, make sure you don't use any pre-loaded software (or install such software yourself) that supposedly makes the drive "Mac ready". when you use software from just about any manufacturer for their storage device you run the risk of that same software not being compatible with macOS updates / upgrades. it can cause the software to stop working. at best this will cause you a headache. at worst it can render your data inaccessible. it is always best to use disk utility to erase and format a drive before use to remove any preloaded software.

please see Erase and reformat a storage device in Disk Utility on Mac - Apple Support

but as far as a recommendation on a specific drive, I personally like the Samsung T7 SSD.

Most any 2.5” SATA SSD will work.

I have PNY and Crucial SSDs in several older Mac mini’s, plus a half dozen others in external enclosures and they are all still going strong.

The choice in the end is totally up to you.