All 3. Id definitely call it an if-then situation though.
Certain vendors carry a reputation for having long captive aquaculture varieties so you can buy with confidence that you’re getting something without pests and of direct lineage. A vendors quarantine practices and how tight their systems run is 99% why id choose to purchase from them or not. Has very little to do with the coral itself.
Specimen name is important. Some say it has gotten out of hand, but it is a useful tool if you want something specific. You can’t say “I want a SCOP, but I hate brand names so I’ll hunt for random bargain bin $5 per frag acros at the lfs and hope I get lucky!” If you want SCOP, buy it from a reputable vendor or trusted source. Only SCOP will be SCOP. Or any other specific subspecies color morph you’re after.
Pictures are probably least important. You can pretty much KNOW that many vendors have been working on some “new release” pieces for years before they bring them to the public. They’re still very much first generation aquaculture and your odds of pulling the same colors will be slim, even under terrific conditions. Not naming names. Some vendors also apply liberal use of saturation boosting, black backdrop, and every other photo technique available to make up the coral into something that will sell it reliably, but not likely be something most keepers can reproduce to the naked eye
