I would insist on seeing a full SMART Health report which will be able to give you critical information about the hard drive which includes whether it has any bad blocks (most common cause of hard drive failures) and the number of power on hours. When using a Mac, DriveDx is the nicest app for gathering & presenting the information because it has an easy to read text report option which also includes some extra details other similar utilities may omit. On Windows, the GSmartControl app (free open source & has a portable version so no install is necessary) provides a nice text report of a drive's health information as well.
It helps to understand how to read & interpret this health report since half of the health information is typically worthless, but sometimes there may still be other clues in the report. Normally I focus on about 6 or 8 health attributes since they are known to correlate to a failing hard drive. However, not all drive issues will show up in this report. In my personal experience though, 95% (probably higher) will probably be fine. I'm talking about the actual drive within the external enclosure & not the external enclosure itself.
For a 3.5" hard drive, you definitely don't want to have one with more than 20K power on hours. Historically a 3.5" hard drive would be fine up to 80K hours, but any more 60K hours may be the limit depending on the drive & how it was used. For a portable drive that is carried around, the life expectancy of a drive is usually much less since they tend to experience impacts from being moved around. I know with 2.5" laptop drives (inside a laptop), many barely make it 6K hours. Talking about impacts, I would want to have the "smartctl" utility which both of the drive health apps I previously mention utilize to run a "conveyance" self test which is meant to identify damage during transport.
As the others have mentioned, you definitely want to erase the whole physical drive using Disk Utility so that a fresh partition table & file system are created. However, you may want to perform a secure erase which involves writing zeroes to every part of the drive to destroy all of the previous data (who knows what may be on it, could be something illegal or personal), plus it would allow you to test the drive to make sure it works. After performing a secure erase, I would run DriveDx to check the health of the drive to make sure the secure erase did not cause any errors in the health report. I would make sure to run DriveDx when you first receive the drive so you can compare the health report with the one the seller provides to you to ensure you have received the same drive & the health information matches (or is close).
