Occasionally I back-up to an external enclosure, so at least I have something stored away from the laptop, but for routine Time Machine stuff I use a micro SD card. I don't use the slot for anything else so it really is is 'fit and forget'. No cables, no fuss and no loss of portability.
I have a Samsung 1TB SSD in an Inateck USB3 enclosure that does UASP. I don't use it for backup. I use it on multi week photo trips for storing any raw files that don't fit on the internal SSD. Backup is made with a portable 2TB portable hard disk when on the road. When home all the data files are moved to the external LaCie library RAID and with backup to a LaCie 6TB D2 drive.
With 512 GB internal memory, look for a SSD with 600GB plus capacity, Just about any name brand SSD is good, the higher prices ones provide better read/write performance which you don't need for backup. Check review at Newegg, B&H, amazon for anyones with issues.
Put the drive in a USB enclosure and set it as the destination. Picking a reliable 2.5 inch enclosure is the hard part as USB is a wild west. You want one that supports sleep. The 2.5 enclosures seem to have fewer issues, however. USB2 may be more reliable and certainly OK for backup. I have a couple $7 ornico that work fine after a firmware update. My startechs have been solid but they are maybe $20.
If you want no hassle and money is not much of an obstacle, pick any one of the SSD thunderbolt external drives.
As others have mentioned, you don't need an SSD for an external backup drive. A spinning HDD will do fine.
Some other thoughts:
You -do- need a 2.5" form factor drive, that is easy to carry along with you if you're traveling.
You -do- need to use a cloning app (such as CarbonCopyCloner or SuperDuper) to maintain a fully-bootable backup that is "ready for immediate use" if you're traveling and experience an "I can't boot!" moment with the internal drive.
If you were using only a Time Machine backup, and had booting problems with the MacBook, you can get going again, but doing so will be more problematical and take a considerable amount of time.
With a cloned bootable backup, just connect it, and you're back in business...